summary statistics

  # Data 
 str(head(mkt_Data[,-c(1,2,3,4,5,6,7,8,7)]))

## Classes 'tbl_df', 'tbl' and 'data.frame':    6 obs. of  15 variables:
##  $ Brand               : chr  "RJ" "RB" "RX" "RX" ...
##  $ Order Number        : num  2.02e+09 2.02e+09 2.02e+09 2.02e+09 1.50e+08 ...
##  $ Order Date          : POSIXct, format: "2018-05-10" "2017-03-10" ...
##  $ Order Quantity      : num  1 13 51 6 54 2
##  $ Promotion Order Doll: num  31.9 1120.2 3555.3 398.3 3813.8 ...
##  $ Promotion           : num  70 59 57 70 114782 ...
##  $ External Description: chr  "Other" "UP3" "NASC150" "Other" ...
##  $ Ship Sets           : chr  "S" "S" "S" "S" ...
##  $ From Date           : POSIXct, format: "2018-05-01" "2017-01-03" ...
##  $ To Date             : POSIXct, format: "2018-05-31" "2017-03-31" ...
##  $ city                : chr  "OKLAHOMA CITY" "SOUTHLAKE" "LOS ANGELES" "SPRINGFIELD" ...
##  $ state               : chr  "OK" "TX" "CA" "OH" ...
##  $ zip                 : chr  "73170" "76092" "90066-4923" "45503" ...
##  $ Qt                  : chr  "Q2_18" "Q1_17" "Q2_17" "Q4_17" ...
##  $ KUNNR_NEW           : chr  "1256111" "1258760" "1251146" "1262300" ...

 summary((mkt_Data[,-c(1,2,3,4,5,6,7,8,7)]))

##     Brand            Order Number         Order Date                 
##  Length:5000        Min.   :1.481e+08   Min.   :2017-01-03 00:00:00  
##  Class :character   1st Qu.:2.016e+09   1st Qu.:2017-06-29 00:00:00  
##  Mode  :character   Median :2.018e+09   Median :2018-01-17 00:00:00  
##                     Mean   :1.578e+09   Mean   :2017-12-31 19:47:42  
##                     3rd Qu.:2.020e+09   3rd Qu.:2018-06-22 00:00:00  
##                     Max.   :2.402e+09   Max.   :2018-12-29 00:00:00  
##  Order Quantity   Promotion Order Doll   Promotion     
##  Min.   :  1.00   Min.   :    0.0      Min.   :    14  
##  1st Qu.:  5.00   1st Qu.:  343.9      1st Qu.:    68  
##  Median : 10.00   Median :  737.1      Median :   106  
##  Mean   : 14.68   Mean   : 1102.9      Mean   : 27220  
##  3rd Qu.: 18.00   3rd Qu.: 1367.1      3rd Qu.:   241  
##  Max.   :690.00   Max.   :41197.7      Max.   :114916  
##  External Description  Ship Sets           From Date                  
##  Length:5000          Length:5000        Min.   :2017-01-03 00:00:00  
##  Class :character     Class :character   1st Qu.:2017-06-01 00:00:00  
##  Mode  :character     Mode  :character   Median :2018-01-01 00:00:00  
##                                          Mean   :2017-12-01 03:56:44  
##                                          3rd Qu.:2018-06-01 00:00:00  
##                                          Max.   :2018-10-01 00:00:00  
##     To Date                        city              state          
##  Min.   :2017-03-31 00:00:00   Length:5000        Length:5000       
##  1st Qu.:2017-07-05 00:00:00   Class :character   Class :character  
##  Median :2018-01-31 00:00:00   Mode  :character   Mode  :character  
##  Mean   :2018-01-30 05:17:05                                        
##  3rd Qu.:2018-07-30 00:00:00                                        
##  Max.   :2018-12-31 00:00:00                                        
##      zip                 Qt             KUNNR_NEW        
##  Length:5000        Length:5000        Length:5000       
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character  
##                                                          
##                                                          
## 

 head(mkt_Data[,-c(1,2,3,4,5,6,7,8,7)])

 describe.by(custA)

## Warning: describe.by is deprecated. Please use the describeBy function

## Warning in describeBy(x = x, group = group, mat = mat, type = type, ...):
## no grouping variable requested

visualization

ggplot(custAG,mapping = aes(x=KUNNR_NEW ,y= order_unit, color=Qt)) + geom_point()

ggplot(custAG[which(custAG$order_unit<= 100),],mapping = aes(y=KUNNR_NEW ,x= order_unit, color=Qt)) + geom_point() + facet_wrap(~Qt,ncol = 2) + ggtitle("Ordered Unit < 150 by Customer ") + ylab("Customer")

ggplot(custAG[which(custAG$order_unit> 100),],mapping = aes(y=KUNNR_NEW ,x= order_unit, color=Qt)) + geom_point() + facet_wrap(~Qt,ncol = 2) + ggtitle("Ordered Unit >150 by Customer ") + ylab("Customer") 

# Graph by Plotly 
plot_ly(data=custAG,y=custAG$order_unit ,x= custAG$KUNNR_NEW,color=custAG$Qt, type= "scatter") %>% layout(   title = "scatter plot: Customer Order Qty by Quarter")

## No scatter mode specifed:
##   Setting the mode to markers
##   Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode

# plot_ly(data=custAG,y=custAG$order_unit ,x= custAG$KUNNR_NEW, z = custAG$Qt ,color=custAG$Qt, type= "scatter3d" )



custAG %>%
  group_by(Qt) %>% summarise(order_unit = sum(order_unit)) %>% 
  ggplot(mapping = aes(x= Qt,y=order_unit,fill = Qt)) + geom_col() +  geom_label(aes(label=order_unit))+
theme_light() +  ggtitle("Order Quantity Over Each Quarter") +ylab("Ordered Unit") + xlab("Quarter")

# Line plot with multiple groups
custAG[order(custAG$seq),] %>%
ggplot( aes(x= seq, y=order_unit, group= KUNNR_NEW,color=Qt) )+
  geom_line()+
  geom_point() + ggtitle("Customer Order Qty Movement over Quarter")

Using Simulation

#Multiple simulation
#Doing multiple check 
rm(p_chi)

## Warning in rm(p_chi): object 'p_chi' not found

p_chi <- data.frame(Qt12= rep(0, 50),Qt23= rep(0, 50),Qt34= rep(0, 50))
for(i in 1:50){
  
   chi_test <- custA[sample(1:nrow(custA),10),c(2,4)]   %>% 
             chisq.test()
  p_chi$Qt12[i]  <- chi_test$p.value
  
  chi_test <- custA[sample(1:nrow(custA),10),c(4,6)]   %>% 
             chisq.test()
  p_chi$Qt23[i]  <- chi_test$p.value
  
  
  
  chi_test <- custA[sample(1:nrow(custA),10),c(6,8)]   %>% 
             chisq.test()
  
  p_chi$Qt34[i]  <- chi_test$p.value
  # samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p))
  # p_hats[i] <- sum(samp == "atheist")/n
}

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

## Warning in chisq.test(.): Chi-squared approximation may be incorrect

# "Chi-squared approximation may be incorrectChi-squared "   The warning message found in the solution above is due to the small cell values in the contingency table. 
#lets check the key
table(gather(p_chi)$key)

## 
## Qt12 Qt23 Qt34 
##   50   50   50

#Gather the data so that we can plot on it.
#using geom_jitter to add some noise as most of poits would overlap in normal plot.
gather(p_chi) %>% ggplot(mapping = aes(x= key, y= round(value,3))) + geom_point()+geom_jitter()

gather(p_chi)%>% filter(value > 0.05)

#contigency table 

 rowSums(custA[,-c(1)])

##    [1]  13  16  31  99   9  16  12  44  17  14  22  18  27  29  41  19  21
##   [18]  12  33  16   9  39  23  20  31  17  29  14  17  19  26   8  22  15
##   [35]  24  42  18  22  17  28  21  29  36  14  17  29  29  44  19  26  14
##   [52]  16  12  31  17  42   9  34  26   9   8  27  27  35  15  34  19  11
##   [69]  21  24  19  28   9  19   8  23   8  13  11  25  99   8  12  20  33
##   [86]  21  41  21  15  26  14  15 164  81  29  11  10  11  19  11  38  23
##  [103]  26  11  30  10  30  17  24  17  15  13  17  17  10  18  17  18  36
##  [120]  68  14  27  36  14  17  13   8   8  15  28  14  32  16  21  17  38
##  [137]  10  12  28  15  15  14  12   8  11  21  13  73   8  11  81  24  32
##  [154]  22  18  12  37  13  25  22   8  18  15  47  41  98   8  17   8  22
##  [171]  31  19  21   8  21  17   9  23  53  66  37   9  13  32  20  15  14
##  [188]  61  13  20 126  58 179  23  24  20  54  23  21  22  27   8  26  14
##  [205]  69  13  18  10  22  25  42 160  38  14  27  17  16  27  12  67  47
##  [222]  22  48  17   9  51   8  12  41  30  15  28  35  17  20  11  24  13
##  [239]  13  26  10  19  15  62  26  65  20  14  20  48  44  26  16  17  37
##  [256]  44  17  10  23  46   8  14  17  45  15  19   8  14   9  26  25  25
##  [273]   8  23  22  36  20  14  53  21  45  32  20  23  13   9  13  27  15
##  [290]  10  17  32  12  19  11  21  28  43  11  48  14  25  28  15  14  12
##  [307]  12  20  11  39  16  22  42  32  21  20  42  20  10  26  30  17  12
##  [324]  28  13  40  35  43  34  59  24  25  10  15  29  31  16  36  16  13
##  [341]  12  28  21  21  24  38  12  17  10  19  13  12  21  32  12  13  34
##  [358]  10  47  37  32  14  24  13  47  17  11  26  29  31  19  20  22  58
##  [375]  17  19  17  36  34  12   9   9  35  23   8  16  35  25 121  23  22
##  [392]  30  44  13  33  10  23  37  19  15  20  18  28  59  12  31  17  12
##  [409]  12  35  27  19  13  22   8  19  12  16  15  16  54  27  25  13  13
##  [426]  46  13   9  25  16  22   8  17  35  13  13  50  23  17  25  15  47
##  [443]  27  20  27  16  14  87  24  39  14  16  13  26  38  38  13  17  21
##  [460]  21  13  62  32  32  17  91  34  30  37  23  20  28  17  12  24  26
##  [477]   8  15  36  14  10  55  11  16  53  17  67   8  36  10  20  13  41
##  [494]  24  22  21  81  20  23  39  16  26  18  22  26  38   9   9  10  27
##  [511]  22  38  25  14  32  18  20 163  11  46  56  14  20   8  13  10  48
##  [528]  13  55  10  26  13  61  20  12  94  21  31  19  37   9  10  10  22
##  [545]  41  15  28  27  18   8  37  30  13  37  39  20  32  22  26  12  44
##  [562]  14  27  18  11  28  13  18  21 146  34   9  20  15  11  11  19  15
##  [579]  26  41  34  19  23  26   8  26  21  14  12  37  42  20  25  29  22
##  [596]  13  26  29  12  27  11  33  17  15  35  22   8  18  25  18  19  13
##  [613]  19  10  24  19  57  75  17  12  37  12  18  12  41  21  74  41  17
##  [630]  21  21  27  14  16  31  27  10  20  11  28  31   9  79  15  25  37
##  [647]   8  20  32  25  18   8  13  16  21  97  47  31  27  15  12  49  13
##  [664]  23  16  11  33  37  27   9  12  30  40  11  11  20  12  12  19  49
##  [681]   8  14  38  17  19  16  15  43  15  37  18  17  10  14  46  31 120
##  [698]  10  35  43  17  24  14  27  54  35  26  19  35  19  27  33  26  17
##  [715]  18  13  65   8  17  35   8  10  23  13  33  11   9  16  17  27  32
##  [732]  15  16  11  41  47  17  22  22  13  20  17   9  11  22  13  63  25
##  [749] 717  27   8   8  60  18  32  24  24  23  18  20  25  22  11  15  13
##  [766]  27  47   8  10  32  25  13  27  16  14  28   8  15  15  11  12  35
##  [783]  14  14  30   9  33  17  12  13  20  24  95  27  78  21  31  24  10
##  [800]  25  19  21  27  13  12  47  35  16  17   8  39  30  38  20  10  17
##  [817]  19  16  10  27  23  27  12  15  28  16  68  25   9  12  33  19  20
##  [834]  33  37  14  10  22  22  19  25 227  19  22  52  14  13   9  12  16
##  [851]  17  12  11  27  11  32  33  15  31  15  37   8   9  17  61  13  11
##  [868]  21  18  13  14  93   8 122  19  19  19  13  14  14  31  37   8  62
##  [885]  36  21  14  28  94  11  26  13  22  15  33  19  10  27  12  19  11
##  [902]   9  31  15  29 120  14  17  23  32  17  31  29  23  13  40   9  31
##  [919]  26  14  10  19  21   9  16  18  19  14  17  13 114  20  43  13  18
##  [936]  13  19  16  35  13  22   8  26  17  14  16  17  21  12  12  22  32
##  [953]  27  23   8  20  16   8   8  15  35  31  18  16  25   9  12  13   8
##  [970]  39   8  13  19  24  17  20  32  19  20  22  20  20  18  25  34  12
##  [987]  51  17  19  13  17  20  11  18  27   9  27   8  18  12

 colSums(custA[,-c(1)])

## Q1_17 Q1_18 Q2_17 Q2_18 Q3_17 Q3_18 Q4_17 Q4_18 
##  3438  3399  3660  3143  3388  2911  2841  2870

4. interpret results.

Since p-value = chi_custA$p.value , which is less than .05 so we can reject the null hypothesis. So we see there is dependancy in the spending over the quarter. Multiple simulation also indicatess pvlaue < 0.05 , for Aplha = 0.5 it indicates that we are 95% confident that spending over each quater is depended on spending over last quarter.

Limitation : We can’t evalaute spending is more or less using Chi-square test , as it is goodness of fittest only.

Build Data and Summary

Lets evaluate Promotion and qty realtion Qt.

# Creating subset of data 
lm_cust <- mkt_Datalean[,c(15,4,1,3,5,7,11,12,13,14)]
lm_cust<- rename(lm_cust , promo = `External Description` )
lm_cust$KUNNR_NEW = as.character(lm_cust$KUNNR_NEW)
lm_cust$Brand = as.factor(lm_cust$Brand)
lm_cust$zip = as.factor(lm_cust$zip)
lm_cust$city = as.factor(lm_cust$city)
lm_cust$state = as.factor(lm_cust$state)
lm_cust$Qt = as.factor(lm_cust$Qt)


# Check data 
head(lm_cust)

summary(lm_cust)

##   KUNNR_NEW         Order Quantity       Brand     
##  Length:5000        Min.   :  1.00   RB     : 752  
##  Class :character   1st Qu.:  5.00   RX     : 713  
##  Mode  :character   Median : 10.00   OO     : 357  
##                     Mean   : 14.68   OX     : 346  
##                     3rd Qu.: 18.00   RY     : 304  
##                     Max.   :690.00   HC     : 286  
##                                      (Other):2242  
##    Order Date                  Promotion Order Doll    promo          
##  Min.   :2017-01-03 00:00:00   Min.   :    0.0      Length:5000       
##  1st Qu.:2017-06-29 00:00:00   1st Qu.:  343.9      Class :character  
##  Median :2018-01-17 00:00:00   Median :  737.1      Mode  :character  
##  Mean   :2017-12-31 19:47:42   Mean   : 1102.9                        
##  3rd Qu.:2018-06-22 00:00:00   3rd Qu.: 1367.1                        
##  Max.   :2018-12-29 00:00:00   Max.   :41197.7                        
##                                                                       
##           city          state           zip             Qt      
##  HOUSTON    :  88   CA     :1003   92683  :  18   Q1_18  : 730  
##  BROOKLYN   :  53   TX     : 581   77494  :  12   Q2_18  : 688  
##  LOS ANGELES:  51   NY     : 363   33131  :  11   Q1_17  : 671  
##  MIAMI      :  49   FL     : 282   90006  :  11   Q3_18  : 627  
##  LAS VEGAS  :  37   PA     : 181   33901  :  10   Q3_17  : 607  
##  SAN DIEGO  :  37   (Other):2580   (Other):4937   Q2_17  : 587  
##  (Other)    :4685   NA's   :  10   NA's   :   1   (Other):1090

# lm_cust[which(is.na(lm_cust$state)),]

lm_cust <- lm_cust %>% group_by(KUNNR_NEW,Qt,Brand,`Order Date`,promo,city,state) %>% summarise(Order_Qty = sum(`Order Quantity`),Doll_Val = sum(`Promotion Order Doll`))

## Warning: Factor `state` contains implicit NA, consider using
## `forcats::fct_explicit_na`

# 
# lm_cust[which(lm_cust$Brand=="OO"),] %>% ggplot(mapping = aes(x= promo, y= Order_Qty,group= Qt , color = Qt)) + geom_line()+
#   geom_point() + geom_jitter()+ facet_grid(year(`Order Date`)~ .)
# 
#  ggplot(lm_cust,mapping = aes(x= Qt, y= Order_Qty, group= Brand ,color= Brand )) + geom_line()+
#   geom_point() + geom_jitter()
 
 # Brand by Year 
 lm_cust[which(lm_cust$Brand %in% c("RB","RJ")),] %>% group_by(promo,Brand,Qt,year =year(`Order Date`)) %>%summarise(Order_Qty = sum(Order_Qty)) %>% 
   ggplot(mapping = aes(x=Brand, y = Order_Qty,fill = Qt)) + 
   geom_col()+facet_grid(year~ .)+
   theme(axis.text.x = element_text(angle = 70, hjust = 1)) + 
   scale_y_continuous( labels = scales::number)+
   ggtitle("Brand by Year ") +ylab("Ordered Unit")

 # promo by year and Brand
 
 plotly::ggplotly( lm_cust[which(lm_cust$Brand %in% c("RB")),] %>% group_by(promo,Brand,Qt,year =year(`Order Date`)) %>%summarise(Order_Qty = sum(Order_Qty)) %>% 
   ggplot(mapping = aes(x=promo, y = Order_Qty,fill = Qt)) +
   geom_col( position = "dodge")+facet_grid(Brand+year~ .,scales="free")+
   theme(axis.text.x = element_text(angle = 70, hjust = 1)) + 
   scale_y_continuous( labels = scales::number)+
     ggtitle("Promo by year and Brand ") +ylab("Ordered Unit"))

  #Plotly check
  plotData  <-  lm_cust[which(lm_cust$Brand %in% c("RB")),] %>% group_by(promo,Brand,Qt,month =month(`Order Date`)) %>%summarise(Order_Qty = sum(Order_Qty)) 
  
  
  plot_ly(x = plotData$promo, y = plotData$Order_Qty, mode= "marker", type = "bar", data= plotData, color= plotData$Qt) %>% layout(title="RB Brand Order ")

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

## Warning: 'bar' objects don't have these attributes: 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'hovertemplate', 'textposition', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'

  lm_cust[which(lm_cust$Brand %in% c("RB")),] %>% group_by(promo,Brand,Qt,month =month(`Order Date`)) %>%summarise(Order_Qty = sum(Order_Qty)) 

  linPlot <- lm_cust[which(lm_cust$Brand %in% c("RB","OO")),] %>% group_by(Brand,date = month(`Order Date`) )%>%summarise(OrderQty = sum(Order_Qty))
  
  linPlot <- lm_cust[which(lm_cust$Brand %in% c("RB","OO")),] %>% group_by(Brand,date = (format(`Order Date`, "%Y-%m")) )%>%summarise(OrderQty = sum(Order_Qty))
  
  linPlot <- lm_cust[which(lm_cust$Brand %in% c("RB","OO")),] %>% group_by(Brand,date = (month(`Order Date`)) , year =  year(`Order Date`))%>%summarise(OrderQty = sum(Order_Qty))
  
  
    plot_ly(x= linPlot$date,y= linPlot$OrderQty, color = as.factor(linPlot$Brand) , data = linPlot[which(linPlot$year==2017),], linetype = I("Brand"))

## Warning: The following are not valid linetype codes:
## 'Brand'
## Valid linetypes include:
## 'solid', 'dot', 'dash', 'longdash', 'dashdot', 'longdashdot'

## Warning: The following are not valid linetype codes:
## 'Brand'
## Valid linetypes include:
## 'solid', 'dot', 'dash', 'longdash', 'dashdot', 'longdashdot'

## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors

## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors

    linPlot$year <- as.factor(linPlot$year)
    plot_ly(x= linPlot$date,y= linPlot$OrderQty, color = as.factor(linPlot$year) , data = linPlot[which(linPlot$brand=="RB"),], linetype = "solid")

## Warning: Unknown or uninitialised column: 'brand'.

## Warning: Factor `Brand` contains implicit NA, consider using
## `forcats::fct_explicit_na`

## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

     # linPlot <- lm_cust[which(lm_cust$Brand %in% c("RB","OO","TY")),] %>% group_by(Brand,dateL = `Order Date`)%>%summarise(OrderQty = sum(Order_Qty))
     #  plot_ly(data= linPlot,x= month(linPlot$dateL), y = linPlot$OrderQty,color = linPlot$Brand , linetype = 'dot' )
     
     # str_replace(str_extract(linPlot$dateL[1],"\\d+_\\d{2}"),"_","")
     linPlot <- lm_cust[which(lm_cust$Brand %in% c("RB","OO","TY")),] %>% group_by(Brand,
                          dateL = Qt
                        )%>%summarise(OrderQty = sum(Order_Qty))
     linPlot$Qt <-  as.numeric(str_replace_all(str_extract_all(linPlot$dateL,"\\d+_\\d{2}"),"_",""))
     
     plot_ly(data= linPlot,x= linPlot$Qt, y = linPlot$OrderQty,color = linPlot$Brand , linetype = 'dot' ) %>% layout(title = " Sales by Brand by Quarter")

## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors

## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors

# check if all promotions are running every year
head(table(year(lm_cust$`Order Date`),lm_cust$promo))

##       
##         ANB B2B200 CHANEL PRE CHROME8 CODE F  H15 HC18 LUX40 MVE150 MVENB
##   2017    1      3          3       2     18  240    7   278      1     1
##   2018    0      0          0       0      0    0    0     0      0     0
##       
##        NASC150 NASC75   NB NB20 NB40 OO15 OOX40 OOX60 Other OY12  PB1  PB3
##   2017      19     15   14    3    1    2    26     5   757   20    7    2
##   2018       0      0    0    0    0    0     0     0  1943    0    0    0
##       
##        PERSOL PRE PRE-SELL B PRE-SELL T PRE-SELL V PRE SELL T RB15  RSD
##   2017          2          1          4          3          7   21    6
##   2018          0          0          0          0          0    0    8
##       
##        SUN1 SUN2  SY1 SY100 SY1000  SY2 SY200 SY250  SY5 SYNERGY54 SYVE
##   2017    6    9    0   341      0    0    66     7    0         0    0
##   2018    0    0  242     0     23   33     0   106   34        25   90
##       
##        TSO20  UP1  UP3  VIP VP1200 VPFP150 VPFP200 VPNB VSE20  WC1  WC2
##   2017     2  227  119    0     11       8      51    7     1   73    2
##   2018     0    0    0   28      0       0       0    0     0   24    3
##       
##        Wild Card
##   2017         0
##   2018        39

Model Creation

Try Predicting Quantity based on Known informaiton . Identifying Best model to predict Quantity

# pairs.panels(lm_cust[,c(2,3)])

# Try Predicting Quantity based on Known informaiton . 
# Identifying Best model to predict Quantity 

head(lm_cust)

result <- data.frame(var = 1:10,pval = 1:10, comment=1:10)

result$var <- "A"
result$pval <- "A"
result$comment <- "A" 

# Working With Sample 
set.seed(42672)
 lm_cust_s1 <- lm_cust[sample(nrow(lm_cust),200),]
 lm_cust_s1$month <- month(lm_cust_s1$`Order Date`)
 lm_cust_s1$month <- as.factor(lm_cust_s1$month )
 
 names(lm_cust_s1)

##  [1] "KUNNR_NEW"  "Qt"         "Brand"      "Order Date" "promo"     
##  [6] "city"       "state"      "Order_Qty"  "Doll_Val"   "month"

lm1 <- lm(Order_Qty ~ Qt + Brand + promo + month + state,lm_cust_s1)
summary(lm1)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + Brand + promo + month + state, 
##     data = lm_cust_s1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -35.673  -4.231   0.000   2.601  51.050 
## 
## Coefficients: (4 not defined because of singularities)
##                 Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    -36.46504   23.40782  -1.558   0.1227   
## QtQ1_18         18.00039   24.29936   0.741   0.4607   
## QtQ2_17         18.37125    9.28988   1.978   0.0510 . 
## QtQ2_18         20.93323   23.58605   0.888   0.3771   
## QtQ3_17         22.31441   25.94766   0.860   0.3920   
## QtQ3_18         23.13547   25.00954   0.925   0.3574   
## QtQ4_17         20.79028   25.63396   0.811   0.4194   
## QtQ4_18         25.55953   25.53385   1.001   0.3194   
## BrandAX         -2.22291   16.43417  -0.135   0.8927   
## BrandBB         18.17065   20.39375   0.891   0.3753   
## BrandBE         11.38307   15.89782   0.716   0.4758   
## BrandBV         13.25507   19.94719   0.665   0.5080   
## BrandDG         22.90699   13.35774   1.715   0.0897 . 
## BrandEA         17.22271   15.04887   1.144   0.2554   
## BrandHC         37.07761   13.91419   2.665   0.0091 **
## BrandMK         18.92319   13.77854   1.373   0.1730   
## BrandMU         -8.49975   27.25828  -0.312   0.7559   
## BrandOJ         10.34942   16.85203   0.614   0.5406   
## BrandOO         19.00698   12.96248   1.466   0.1460   
## BrandOX         28.20339   13.14453   2.146   0.0345 * 
## BrandOY         13.88347   14.51767   0.956   0.3414   
## BrandPH         20.20884   14.28289   1.415   0.1605   
## BrandPO         32.50025   18.97884   1.712   0.0902 . 
## BrandPR         30.68086   13.46828   2.278   0.0250 * 
## BrandPS         15.15263   15.71143   0.964   0.3374   
## BrandRA         12.86219   13.64030   0.943   0.3482   
## BrandRB         21.61683   12.22194   1.769   0.0803 . 
## BrandRJ         10.98168   16.90526   0.650   0.5176   
## BrandRL         18.91419   14.70578   1.286   0.2016   
## BrandRX         27.52025   12.74336   2.160   0.0334 * 
## BrandRY          9.72803   11.97928   0.812   0.4188   
## BrandSF        -19.48943   20.06241  -0.971   0.3339   
## BrandTF         27.51580   14.93427   1.842   0.0686 . 
## BrandTY         10.20080   18.39706   0.554   0.5806   
## BrandVE         19.25721   13.07980   1.472   0.1444   
## BrandVO         15.23984   17.08040   0.892   0.3746   
## promoH15        -1.62030   15.93106  -0.102   0.9192   
## promoLUX40      11.75592   17.30055   0.680   0.4985   
## promoNASC75     19.41953   23.00442   0.844   0.4008   
## promoNB         12.57707   19.19284   0.655   0.5139   
## promoOOX40       8.29981   20.65580   0.402   0.6888   
## promoOther      -8.26783   28.79134  -0.287   0.7746   
## promoOY12       25.30624   23.55245   1.074   0.2854   
## promoPB1        36.87749   29.68013   1.242   0.2172   
## promoRB15       32.57282   23.85811   1.365   0.1755   
## promoRSD        19.17100   39.07783   0.491   0.6249   
## promoSUN2       15.54299   26.06557   0.596   0.5524   
## promoSY1        -1.34877   29.26186  -0.046   0.9633   
## promoSY100      -4.94784   29.50864  -0.168   0.8672   
## promoSY1000    -11.99035   34.35517  -0.349   0.7279   
## promoSY2         0.40351   31.32019   0.013   0.9897   
## promoSY200      18.21825   20.17638   0.903   0.3689   
## promoSY250      25.08751   30.41952   0.825   0.4117   
## promoSY5        11.36126   34.55088   0.329   0.7430   
## promoSYVE       -4.38441   31.90636  -0.137   0.8910   
## promoUP1        -2.14988   16.43054  -0.131   0.8962   
## promoUP3        -2.70304   17.76997  -0.152   0.8794   
## promoVIP         9.09819   32.99633   0.276   0.7834   
## promoVPNB       10.38062   20.70836   0.501   0.6174   
## promoWC1        18.58697   18.86336   0.985   0.3270   
## promoWC2         5.27787   24.31924   0.217   0.8287   
## promoWild Card   1.73126   33.96237   0.051   0.9595   
## month2          16.65961    6.60551   2.522   0.0134 * 
## month3          15.88870    7.07670   2.245   0.0272 * 
## month4          -0.37627    6.58180  -0.057   0.9545   
## month5          -2.09586    7.83357  -0.268   0.7896   
## month6                NA         NA      NA       NA   
## month7           3.19081    6.74421   0.473   0.6372   
## month8          -1.95339    5.84180  -0.334   0.7389   
## month9                NA         NA      NA       NA   
## month10         -4.94403    7.30411  -0.677   0.5002   
## month11         -0.06341    7.12405  -0.009   0.9929   
## month12               NA         NA      NA       NA   
## stateAZ         16.48838   20.33711   0.811   0.4196   
## stateCA         12.05055   11.67329   1.032   0.3046   
## stateCO         16.86173   13.42809   1.256   0.2124   
## stateCT          9.25895   13.85852   0.668   0.5057   
## stateFL         17.80283   12.36884   1.439   0.1535   
## stateGA          8.42038   13.33407   0.631   0.5293   
## stateIA         42.20359   18.67097   2.260   0.0262 * 
## stateID          7.79968   15.68725   0.497   0.6202   
## stateIL          7.97249   12.61030   0.632   0.5288   
## stateIN          2.27695   13.43487   0.169   0.8658   
## stateKS          0.64039   17.64006   0.036   0.9711   
## stateKY          7.61863   13.25988   0.575   0.5670   
## stateLA         20.35612   16.98149   1.199   0.2337   
## stateMA         16.30341   13.31618   1.224   0.2240   
## stateMD         10.18281   19.31153   0.527   0.5993   
## stateME          5.98689   17.51323   0.342   0.7332   
## stateMI         15.33782   14.10445   1.087   0.2797   
## stateMO          8.71079   13.97244   0.623   0.5345   
## stateMS         12.04992   16.12025   0.748   0.4567   
## stateNC          0.85877   14.63154   0.059   0.9533   
## stateNE         11.05145   15.70960   0.703   0.4835   
## stateNH         14.09508   15.65536   0.900   0.3703   
## stateNJ          7.86700   14.03057   0.561   0.5764   
## stateNM          5.39523   16.00708   0.337   0.7368   
## stateNV         17.62102   14.53551   1.212   0.2285   
## stateNY         15.54457   12.17271   1.277   0.2048   
## stateOH          9.27533   13.50044   0.687   0.4938   
## stateOK          9.83495   13.88873   0.708   0.4807   
## stateOR         -5.41943   22.72746  -0.238   0.8121   
## statePA          9.97787   12.64259   0.789   0.4320   
## statePR         15.88840   14.82491   1.072   0.2866   
## stateRI               NA         NA      NA       NA   
## stateTN         12.86440   16.19163   0.795   0.4289   
## stateTX         10.79331   11.72175   0.921   0.3596   
## stateUT         11.65310   19.84770   0.587   0.5586   
## stateVA         18.44788   19.48008   0.947   0.3461   
## stateWA         19.71919   16.14748   1.221   0.2251   
## stateWI          7.38835   16.26748   0.454   0.6508   
## stateWV         27.63151   21.56170   1.282   0.2032   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.84 on 92 degrees of freedom
## Multiple R-squared:  0.5322, Adjusted R-squared:  -0.01177 
## F-statistic: 0.9784 on 107 and 92 DF,  p-value: 0.5452

anova(lm1)

result$var[1] <- "lm(formula = Order_Qty ~ Qt + Brand + promo + month + state, 
    data = lm_cust_s1)"
result$pval[1] <-  "Adjusted R-squared:  0.2356 F-statistic: 1.568 on 108 and 91 DF,  p-value: 0.01388"

result$comment[1] <- "(Month , State ) Qt,Promo codes are significant,state is not " 


#Dropping State

lm2 <- lm(Order_Qty ~ Qt + Brand + promo + month,lm_cust_s1)
summary(lm2)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + Brand + promo + month, data = lm_cust_s1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.383  -5.780   0.000   3.595  53.573 
## 
## Coefficients: (3 not defined because of singularities)
##                 Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    -12.49704   14.63275  -0.854  0.39465   
## QtQ1_18         12.18308   18.91116   0.644  0.52056   
## QtQ2_17          8.30689    6.61006   1.257  0.21111   
## QtQ2_18         11.99134   18.66270   0.643  0.52166   
## QtQ3_17         16.32355   19.88174   0.821  0.41313   
## QtQ3_18         15.75627   19.51636   0.807  0.42095   
## QtQ4_17         13.88639   19.94766   0.696  0.48758   
## QtQ4_18         20.44311   19.83325   1.031  0.30457   
## BrandAX         -5.90175   13.84548  -0.426  0.67062   
## BrandBB         16.40336   17.22325   0.952  0.34266   
## BrandBE          5.53851   13.56604   0.408  0.68375   
## BrandBV         12.67011   16.80670   0.754  0.45229   
## BrandDG         18.89818   11.38464   1.660  0.09933 . 
## BrandEA         12.65017   12.85487   0.984  0.32691   
## BrandHC         35.90515   11.85869   3.028  0.00297 **
## BrandMK         10.29752   11.62513   0.886  0.37736   
## BrandMU        -14.39136   24.54561  -0.586  0.55868   
## BrandOJ          3.69422   14.05848   0.263  0.79314   
## BrandOO         14.84016   10.86683   1.366  0.17441   
## BrandOX         20.89679   10.90196   1.917  0.05746 . 
## BrandOY          9.65762   11.69246   0.826  0.41033   
## BrandPH         12.84702   11.53395   1.114  0.26740   
## BrandPO         26.60864   16.77271   1.586  0.11507   
## BrandPR         25.24977   11.56601   2.183  0.03082 * 
## BrandPS         11.41966   12.97302   0.880  0.38034   
## BrandRA          8.67947   11.75566   0.738  0.46165   
## BrandRB         17.81507   10.35035   1.721  0.08759 . 
## BrandRJ          3.51047   13.87317   0.253  0.80064   
## BrandRL         10.99017   11.89269   0.924  0.35714   
## BrandRX         22.17050   10.74071   2.064  0.04099 * 
## BrandRY          7.47817   10.44905   0.716  0.47547   
## BrandSF        -19.53713   16.67908  -1.171  0.24360   
## BrandTF         21.66324   12.40692   1.746  0.08316 . 
## BrandTY         11.08892   14.15169   0.784  0.43471   
## BrandVE         13.83746   10.79166   1.282  0.20204   
## BrandVO          5.97036   12.74835   0.468  0.64034   
## promoH15         0.47269   11.02617   0.043  0.96587   
## promoLUX40      10.53215   10.74763   0.980  0.32893   
## promoNASC75     21.05516   17.12019   1.230  0.22098   
## promoNB          5.83877   13.24998   0.441  0.66019   
## promoOOX40       8.42342   12.50389   0.674  0.50172   
## promoOther      -7.16441   21.25078  -0.337  0.73656   
## promoOY12       14.83942   17.22027   0.862  0.39042   
## promoPB1        11.65687   16.34348   0.713  0.47697   
## promoRB15       20.31504   16.93654   1.199  0.23252   
## promoRSD         5.31312   25.89650   0.205  0.83776   
## promoSUN2       19.58150   20.90827   0.937  0.35073   
## promoSY1        -3.99612   21.60869  -0.185  0.85357   
## promoSY100      -5.12616   21.83491  -0.235  0.81476   
## promoSY1000     -6.65029   25.74083  -0.258  0.79654   
## promoSY2         2.06180   23.17502   0.089  0.92925   
## promoSY200      15.45106   14.45747   1.069  0.28717   
## promoSY250      23.85974   22.71510   1.050  0.29549   
## promoSY5         8.27890   26.27859   0.315  0.75323   
## promoSYVE       -5.37083   25.18542  -0.213  0.83146   
## promoUP1        -4.34772   10.49617  -0.414  0.67940   
## promoUP3        -5.97238   11.28390  -0.529  0.59751   
## promoVIP        11.96719   26.11733   0.458  0.64757   
## promoVPNB        6.11156   15.05503   0.406  0.68545   
## promoWC1        13.86758   12.70899   1.091  0.27722   
## promoWC2         9.60890   16.68194   0.576  0.56561   
## promoWild Card  -4.55881   24.69039  -0.185  0.85380   
## month2          13.06606    5.17905   2.523  0.01285 * 
## month3           8.99134    5.20897   1.726  0.08670 . 
## month4           0.29752    4.88696   0.061  0.95155   
## month5           0.06004    5.99863   0.010  0.99203   
## month6                NA         NA      NA       NA   
## month7           3.22993    5.69877   0.567  0.57184   
## month8          -1.70347    4.70572  -0.362  0.71794   
## month9                NA         NA      NA       NA   
## month10         -6.88822    5.86657  -1.174  0.24248   
## month11         -2.75016    5.60855  -0.490  0.62471   
## month12               NA         NA      NA       NA   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.67 on 130 degrees of freedom
## Multiple R-squared:  0.4455, Adjusted R-squared:  0.1512 
## F-statistic: 1.514 on 69 and 130 DF,  p-value: 0.0217

anova(lm2)

result$var[2] <- "lm(formula = Order_Qty ~ Qt + Brand + promo + month, data = lm_cust_s1)"
result$pval[2] <- "Adjusted R-squared:  0.3198 F-statistic: 2.396 on 67 and 132 DF,  p-value: 9.788e-06"
result$comment[2] <- "(Month)Brand is not significant" 

#Promo promoVPFP200 turns out to more significant here. 



#3  Dropping brand info 
lm3 <- lm(Order_Qty ~  Qt + promo + month,lm_cust_s1)
summary(lm3)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + promo + month, data = lm_cust_s1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -25.602  -6.340  -1.794   3.365  71.781 
## 
## Coefficients: (3 not defined because of singularities)
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      4.3586    10.1164   0.431   0.6672  
## QtQ1_18          9.0901    20.0945   0.452   0.6516  
## QtQ2_17          2.2828     6.3014   0.362   0.7176  
## QtQ2_18          6.3740    19.8318   0.321   0.7483  
## QtQ3_17          7.4515    20.8205   0.358   0.7209  
## QtQ3_18          8.8989    20.6177   0.432   0.6666  
## QtQ4_17          7.2990    20.8614   0.350   0.7269  
## QtQ4_18         13.9049    20.9071   0.665   0.5070  
## promoH15         5.6875    11.3996   0.499   0.6185  
## promoLUX40      12.1038    10.7129   1.130   0.2603  
## promoNASC75     24.2221    17.3681   1.395   0.1651  
## promoNB          1.9544    13.8675   0.141   0.8881  
## promoOOX40      16.2523    12.8856   1.261   0.2091  
## promoOther       0.1734    22.4412   0.008   0.9938  
## promoOY12        7.6414    16.9461   0.451   0.6527  
## promoPB1         9.6414    16.9461   0.569   0.5702  
## promoRB15       28.7633    17.6668   1.628   0.1055  
## promoRSD         5.3424    26.6748   0.200   0.8415  
## promoSUN2       14.8586    13.9555   1.065   0.2886  
## promoSY1         3.5060    22.7715   0.154   0.8778  
## promoSY100       4.6518    22.9196   0.203   0.8394  
## promoSY1000      1.9338    26.4809   0.073   0.9419  
## promoSY2         1.0971    24.0691   0.046   0.9637  
## promoSY200       8.3586    13.9555   0.599   0.5501  
## promoSY250      13.1530    23.3349   0.564   0.5738  
## promoSY5        20.2733    26.6890   0.760   0.4486  
## promoSYVE        3.4191    26.5683   0.129   0.8978  
## promoUP1         1.4645    10.7949   0.136   0.8923  
## promoUP3        -2.8850    11.1504  -0.259   0.7962  
## promoVIP         6.2674    25.7634   0.243   0.8081  
## promoVPNB       10.2674    14.2014   0.723   0.4708  
## promoWC1        17.2166    12.6616   1.360   0.1758  
## promoWC2        19.2674    17.1492   1.124   0.2629  
## promoWild Card -12.2574    24.4467  -0.501   0.6168  
## month2           9.6175     5.0470   1.906   0.0585 .
## month3           3.3740     4.8627   0.694   0.4888  
## month4           0.1365     4.8383   0.028   0.9775  
## month5          -1.4046     5.8537  -0.240   0.8107  
## month6               NA         NA      NA       NA  
## month7           3.2291     5.8128   0.556   0.5793  
## month8          -2.6766     4.7424  -0.564   0.5733  
## month9               NA         NA      NA       NA  
## month10         -7.5369     5.9201  -1.273   0.2049  
## month11         -7.2725     5.4414  -1.337   0.1833  
## month12              NA         NA      NA       NA  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.6 on 158 degrees of freedom
## Multiple R-squared:  0.2243, Adjusted R-squared:  0.02301 
## F-statistic: 1.114 on 41 and 158 DF,  p-value: 0.3126

anova(lm3)

result$var[3] <- "lm(formula = Order_Qty ~ Qt + promo + month, data = lm_cust_s1)"
result$pval[3] <- "Adjusted R-squared:  0.2799 F-statistic:  3.09 on 37 and 162 DF,  p-value: 4.911e-07"
result$comment[3] <- "(Month) least significant" 

#4  Dropping Month
lm4 <- lm(Order_Qty ~  Qt + promo ,lm_cust_s1)
summary(lm4)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + promo, data = lm_cust_s1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.200  -6.871  -2.023   3.111  78.800 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      6.51577    9.87084   0.660   0.5101  
## QtQ1_18         10.81104   19.63228   0.551   0.5826  
## QtQ2_17         -2.03155    4.70074  -0.432   0.6662  
## QtQ2_18          3.00000   19.17386   0.156   0.8759  
## QtQ3_17          3.12864   19.69623   0.159   0.8740  
## QtQ3_18          5.16104   19.62113   0.263   0.7928  
## QtQ4_17         -1.40241   19.63734  -0.071   0.9432  
## QtQ4_18          5.42945   19.69608   0.276   0.7832  
## promoH15         7.63683   10.86250   0.703   0.4830  
## promoLUX40      14.58087   10.52887   1.385   0.1680  
## promoNASC75     26.51577   16.77056   1.581   0.1158  
## promoNB          1.48423   13.76018   0.108   0.9142  
## promoOOX40      17.82808   12.40144   1.438   0.1524  
## promoOther       1.32318   21.76394   0.061   0.9516  
## promoOY12        5.48423   16.77056   0.327   0.7441  
## promoPB1         7.48423   16.77056   0.446   0.6560  
## promoRB15       29.51577   16.77056   1.760   0.0803 .
## promoRSD        11.88664   25.82396   0.460   0.6459  
## promoSUN2       17.01577   13.76018   1.237   0.2180  
## promoSY1         3.94435   22.05667   0.179   0.8583  
## promoSY100       7.40239   22.21911   0.333   0.7394  
## promoSY1000      7.67318   25.82011   0.297   0.7667  
## promoSY2         0.05478   23.38037   0.002   0.9981  
## promoSY200      10.51577   13.76018   0.764   0.4458  
## promoSY250      11.87318   22.79525   0.521   0.6032  
## promoSY5        19.05478   25.86866   0.737   0.4624  
## promoSYVE        2.32318   25.81164   0.090   0.9284  
## promoUP1         3.04115   10.44178   0.291   0.7712  
## promoUP3        -0.07819   10.91712  -0.007   0.9943  
## promoVIP         7.48423   25.47329   0.294   0.7693  
## promoVPNB       11.48423   13.76018   0.835   0.4051  
## promoWC1        20.82808   12.40144   1.679   0.0949 .
## promoWC2        20.48423   16.77056   1.221   0.2237  
## promoWild Card -11.32682   23.97434  -0.472   0.6372  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.56 on 166 degrees of freedom
## Multiple R-squared:  0.1895, Adjusted R-squared:  0.02835 
## F-statistic: 1.176 on 33 and 166 DF,  p-value: 0.2514

anova(lm4)

result$var[4] <- "lm(formula = Order_Qty ~ Qt + promo, data = lm_cust_s1)"
result$pval[4] <- "Adjusted R-squared:  -0.003147 F-statistic: 0.9799 on 31 and 168 DF,  p-value: 0.5038"
result$comment[4] <- "not much significant"

# 5 Increase Sample Size
rm(lm_cust_s1)
# SInce I see no major significance increasing the sample size to 500
set.seed(12121)
lm_cust_s2 <- lm_cust[sample(nrow(lm_cust),500),]
 lm_cust_s2$month <- month(lm_cust_s2$`Order Date`)
 lm_cust_s2$month <- as.factor(lm_cust_s2$month )
 names(lm_cust_s2)

##  [1] "KUNNR_NEW"  "Qt"         "Brand"      "Order Date" "promo"     
##  [6] "city"       "state"      "Order_Qty"  "Doll_Val"   "month"

 lm5 <- lm(Order_Qty ~ Qt + Brand + promo + month + state,lm_cust_s2)
summary(lm5)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + Brand + promo + month + state, 
##     data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -33.494  -7.572  -1.467   4.583 259.806 
## 
## Coefficients: (3 not defined because of singularities)
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      20.14325   34.73837   0.580   0.5624  
## QtQ1_18         -12.38201   13.68592  -0.905   0.3662  
## QtQ2_17          -9.46505    6.69384  -1.414   0.1582  
## QtQ2_18         -15.15304   14.22715  -1.065   0.2875  
## QtQ3_17          -9.96147   14.17595  -0.703   0.4827  
## QtQ3_18         -16.39689   14.49849  -1.131   0.2588  
## QtQ4_17         -20.60796   14.37100  -1.434   0.1524  
## QtQ4_18         -12.07142   14.66120  -0.823   0.4108  
## BrandAX          -5.93184   15.11709  -0.392   0.6950  
## BrandBB           1.19151   20.69687   0.058   0.9541  
## BrandBE          -4.78670   14.38799  -0.333   0.7396  
## BrandBV         -22.57412   19.70034  -1.146   0.2526  
## BrandCH         -12.04660   16.94306  -0.711   0.4775  
## BrandDG          -9.85702   14.56936  -0.677   0.4991  
## BrandDY           1.75232   21.38808   0.082   0.9347  
## BrandEA           3.69546   16.12952   0.229   0.8189  
## BrandHC          -1.85858   13.65709  -0.136   0.8918  
## BrandMK          -3.69741   13.90020  -0.266   0.7904  
## BrandMU         -10.78838   16.52074  -0.653   0.5142  
## BrandOJ         -12.23249   21.30963  -0.574   0.5663  
## BrandOO           4.61509   13.57490   0.340   0.7341  
## BrandOX           4.43375   14.25313   0.311   0.7559  
## BrandOY          -6.96381   14.11707  -0.493   0.6221  
## BrandPH         -11.47871   13.98163  -0.821   0.4122  
## BrandPO          -5.07548   19.04164  -0.267   0.7900  
## BrandPP          -5.82629   17.21851  -0.338   0.7353  
## BrandPR          -8.90657   13.50053  -0.660   0.5098  
## BrandPS         -19.72345   14.99779  -1.315   0.1893  
## BrandRA         -12.24210   20.92701  -0.585   0.5589  
## BrandRB           1.50802   13.22393   0.114   0.9093  
## BrandRJ         -14.42184   15.64738  -0.922   0.3573  
## BrandRL         -12.58423   15.60577  -0.806   0.4205  
## BrandRX          -2.99169   13.16636  -0.227   0.8204  
## BrandRY         -14.52809   13.27817  -1.094   0.2746  
## BrandSF         -10.81681   20.58147  -0.526   0.5995  
## BrandTF          -7.81851   14.24592  -0.549   0.5835  
## BrandTY         -14.82686   14.49356  -1.023   0.3070  
## BrandVA           5.07855   21.07170   0.241   0.8097  
## BrandVE          -5.08421   13.92758  -0.365   0.7153  
## BrandVO          -6.53843   14.38871  -0.454   0.6498  
## promoCODE F     -15.70126   26.42017  -0.594   0.5527  
## promoH15         -9.24165   24.63055  -0.375   0.7077  
## promoHC18       -22.87087   37.20216  -0.615   0.5391  
## promoLUX40       -1.03471   24.41081  -0.042   0.9662  
## promoNASC150     -2.99490   29.18787  -0.103   0.9183  
## promoNASC75     -14.83641   33.56867  -0.442   0.6588  
## promoNB         -10.14308   32.38604  -0.313   0.7543  
## promoNB40        13.31739   32.60768   0.408   0.6832  
## promoOO15        -4.58799   33.64289  -0.136   0.8916  
## promoOOX40        9.98885   29.23441   0.342   0.7328  
## promoOther        6.56118   27.49548   0.239   0.8115  
## promoOY12        -1.15356   33.46079  -0.034   0.9725  
## promoPB3         -3.53753   35.79019  -0.099   0.9213  
## promoPRE-SELL T   1.26157   32.82228   0.038   0.9694  
## promoPRE-SELL V   0.04740   42.43947   0.001   0.9991  
## promoPRE SELL T  -5.04635   33.45525  -0.151   0.8802  
## promoRB15        10.77761   28.81100   0.374   0.7086  
## promoRSD         22.70700   35.12479   0.646   0.5184  
## promoSUN1        37.19751   32.74358   1.136   0.2567  
## promoSY1          4.78064   28.00221   0.171   0.8645  
## promoSY100        6.00226   27.68624   0.217   0.8285  
## promoSY1000       4.81309   30.54350   0.158   0.8749  
## promoSY2         -1.52005   29.37528  -0.052   0.9588  
## promoSY200        7.58263   26.44625   0.287   0.7745  
## promoSY250       18.56546   28.33298   0.655   0.5127  
## promoSY5          8.20619   29.56529   0.278   0.7815  
## promoSYNERGY54   -7.00092   28.33806  -0.247   0.8050  
## promoSYVE        16.72686   28.90926   0.579   0.5632  
## promoUP1         -5.89556   24.63619  -0.239   0.8110  
## promoUP3        -13.58070   25.19473  -0.539   0.5902  
## promoVIP         22.49923   29.20433   0.770   0.4416  
## promoVP1200     -25.50758   33.25155  -0.767   0.4435  
## promoVPFP200      7.64224   25.18866   0.303   0.7618  
## promoWC1         23.41038   26.52423   0.883   0.3780  
## promoWild Card    5.08864   31.07607   0.164   0.8700  
## month2           -7.86552    5.24763  -1.499   0.1348  
## month3           -2.84667    5.45975  -0.521   0.6024  
## month4            9.59351    5.09722   1.882   0.0606 .
## month5            7.98950    4.92468   1.622   0.1056  
## month6                 NA         NA      NA       NA  
## month7           -4.03791    5.86721  -0.688   0.4918  
## month8           -1.83638    4.44705  -0.413   0.6799  
## month9                 NA         NA      NA       NA  
## month10           0.19136    5.47634   0.035   0.9721  
## month11          10.02477    5.34592   1.875   0.0616 .
## month12                NA         NA      NA       NA  
## stateAL          -3.86751   25.77620  -0.150   0.8808  
## stateAR           9.43907   26.93737   0.350   0.7262  
## stateAZ           7.19716   22.51918   0.320   0.7495  
## stateCA          10.92148   21.24314   0.514   0.6075  
## stateCO          -1.37323   21.92096  -0.063   0.9501  
## stateCT           1.56498   22.18577   0.071   0.9438  
## stateFL           9.96737   21.37418   0.466   0.6413  
## stateGA           7.76887   21.73436   0.357   0.7210  
## stateGU          55.34930   31.97985   1.731   0.0843 .
## stateHI          -6.02231   24.57447  -0.245   0.8065  
## stateIA          10.34710   24.51255   0.422   0.6732  
## stateID           4.01486   30.18054   0.133   0.8942  
## stateIL           3.39434   21.66533   0.157   0.8756  
## stateIN           0.78569   22.91155   0.034   0.9727  
## stateKS           0.27921   22.68561   0.012   0.9902  
## stateKY           7.01166   22.27732   0.315   0.7531  
## stateLA           6.61282   25.32635   0.261   0.7942  
## stateMA          -3.01567   22.79640  -0.132   0.8948  
## stateMD           8.08368   23.50580   0.344   0.7311  
## stateME          -0.29373   24.35634  -0.012   0.9904  
## stateMI          -1.27804   22.09473  -0.058   0.9539  
## stateMN          -2.29799   23.70904  -0.097   0.9228  
## stateMO          12.37066   22.96224   0.539   0.5904  
## stateMS           2.34391   22.72796   0.103   0.9179  
## stateMT           8.35430   26.06567   0.321   0.7488  
## stateNC           1.91098   21.90083   0.087   0.9305  
## stateND           7.31947   30.77008   0.238   0.8121  
## stateNE          -7.25877   23.64020  -0.307   0.7590  
## stateNH           2.87995   24.84885   0.116   0.9078  
## stateNJ           9.80019   21.78772   0.450   0.6531  
## stateNM          -0.22389   30.65327  -0.007   0.9942  
## stateNV           8.35141   22.64371   0.369   0.7125  
## stateNY           6.17187   21.39072   0.289   0.7731  
## stateOH          -0.02588   22.72123  -0.001   0.9991  
## stateOK          12.51012   22.62553   0.553   0.5807  
## stateOR           5.99219   22.97606   0.261   0.7944  
## statePA          -2.95395   21.82543  -0.135   0.8924  
## statePR          17.22291   22.70442   0.759   0.4486  
## stateRI          -0.15320   29.89626  -0.005   0.9959  
## stateSC          -3.59822   24.04595  -0.150   0.8811  
## stateTN           6.37490   22.92252   0.278   0.7811  
## stateTX           7.12500   21.34097   0.334   0.7387  
## stateUT          -7.04796   23.59811  -0.299   0.7654  
## stateVA          -2.06891   24.60180  -0.084   0.9330  
## stateVT          -3.34033   29.73617  -0.112   0.9106  
## stateWA          -3.16528   23.24011  -0.136   0.8917  
## stateWI          -9.33238   29.88901  -0.312   0.7550  
## stateWV           2.59632   31.03589   0.084   0.9334  
## stateWY          -7.91241   34.21432  -0.231   0.8172  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.4 on 368 degrees of freedom
## Multiple R-squared:  0.2427, Adjusted R-squared:  -0.02682 
## F-statistic: 0.9005 on 131 and 368 DF,  p-value: 0.7576

anova(lm5)

result$var[5] <- "500: lm(formula = Order_Qty ~ Qt + Brand + promo + month + state,     data = lm_cust_s2)"
result$pval[5] <-   " Adjusted R-squared:  0.05218 F-statistic: 1.214 on 128 and 370 DF,  p-value: 0.08366"
result$comment[5] <- "(Sig: Promo) " 
 
#6 Dropping Month, I want to keep state for now.

lm6 <- lm(Order_Qty ~ Qt + Brand + promo + state,lm_cust_s2)
summary(lm6)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + Brand + promo + state, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.127  -7.511  -1.505   4.252 268.474 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)       8.02960   34.30241   0.234   0.8150  
## QtQ1_18          -6.62931   13.58937  -0.488   0.6260  
## QtQ2_17          -0.07944    5.10610  -0.016   0.9876  
## QtQ2_18          -1.41508   13.27754  -0.107   0.9152  
## QtQ3_17          -2.28899   13.36886  -0.171   0.8641  
## QtQ3_18          -8.30409   13.56042  -0.612   0.5407  
## QtQ4_17          -6.47382   12.98965  -0.498   0.6185  
## QtQ4_18          -0.68162   13.61072  -0.050   0.9601  
## BrandAX          -5.24418   15.00420  -0.350   0.7269  
## BrandBB          -1.86942   20.63607  -0.091   0.9279  
## BrandBE          -4.64213   14.36805  -0.323   0.7468  
## BrandBV         -18.47433   19.58435  -0.943   0.3461  
## BrandCH          -9.37833   16.86124  -0.556   0.5784  
## BrandDG          -9.46028   14.48665  -0.653   0.5141  
## BrandDY          -4.62203   21.26211  -0.217   0.8280  
## BrandEA           4.55126   16.10243   0.283   0.7776  
## BrandHC          -0.51819   13.61044  -0.038   0.9696  
## BrandMK          -3.10084   13.86387  -0.224   0.8231  
## BrandMU         -11.10187   16.49254  -0.673   0.5013  
## BrandOJ         -13.02060   21.17600  -0.615   0.5390  
## BrandOO           4.85366   13.50752   0.359   0.7196  
## BrandOX           4.57275   14.23692   0.321   0.7482  
## BrandOY          -6.54991   14.12100  -0.464   0.6430  
## BrandPH         -11.38116   13.96818  -0.815   0.4157  
## BrandPO          -3.99850   19.02848  -0.210   0.8337  
## BrandPP          -7.46227   17.03407  -0.438   0.6616  
## BrandPR          -6.58560   13.46938  -0.489   0.6252  
## BrandPS         -18.00037   14.97084  -1.202   0.2300  
## BrandRA         -13.00028   20.75422  -0.626   0.5314  
## BrandRB           2.15040   13.20372   0.163   0.8707  
## BrandRJ         -15.82872   15.61486  -1.014   0.3114  
## BrandRL         -12.50697   15.55294  -0.804   0.4218  
## BrandRX          -2.03237   13.13140  -0.155   0.8771  
## BrandRY         -13.47718   13.23821  -1.018   0.3093  
## BrandSF          -9.44177   20.51900  -0.460   0.6457  
## BrandTF          -7.34934   14.19749  -0.518   0.6050  
## BrandTY         -15.01981   14.45416  -1.039   0.2994  
## BrandVA           1.38709   21.05845   0.066   0.9475  
## BrandVE          -4.53773   13.92096  -0.326   0.7446  
## BrandVO          -6.22499   14.34452  -0.434   0.6646  
## promoCODE F      -9.25451   26.32037  -0.352   0.7253  
## promoH15         -1.90017   24.55474  -0.077   0.9384  
## promoHC18        -7.70355   36.66452  -0.210   0.8337  
## promoLUX40        4.70290   24.32608   0.193   0.8468  
## promoNASC150      6.83773   29.10439   0.235   0.8144  
## promoNASC75      -5.37040   33.57992  -0.160   0.8730  
## promoNB          -1.95693   32.14311  -0.061   0.9515  
## promoNB40        20.15586   32.26949   0.625   0.5326  
## promoOO15        -3.29398   33.60503  -0.098   0.9220  
## promoOOX40       14.60444   29.06348   0.503   0.6156  
## promoOther        6.84500   27.41425   0.250   0.8030  
## promoOY12        10.59259   32.99069   0.321   0.7483  
## promoPB3          7.05241   35.46387   0.199   0.8425  
## promoPRE-SELL T   2.58398   32.94963   0.078   0.9375  
## promoPRE-SELL V  12.36557   42.42057   0.291   0.7708  
## promoPRE SELL T   4.86633   33.15357   0.147   0.8834  
## promoRB15        14.61887   28.64691   0.510   0.6101  
## promoRSD         25.33896   34.85237   0.727   0.4677  
## promoSUN1        44.96085   32.49578   1.384   0.1673  
## promoSY1          7.74770   27.91065   0.278   0.7815  
## promoSY100        6.84815   27.61190   0.248   0.8043  
## promoSY1000       3.94037   30.33851   0.130   0.8967  
## promoSY2          2.65038   29.32512   0.090   0.9280  
## promoSY200       10.11257   26.29383   0.385   0.7008  
## promoSY250       19.06825   28.19119   0.676   0.4992  
## promoSY5          8.35961   29.37713   0.285   0.7761  
## promoSYNERGY54   -3.04753   28.26101  -0.108   0.9142  
## promoSYVE        17.74689   28.81123   0.616   0.5383  
## promoUP1          1.26964   24.50377   0.052   0.9587  
## promoUP3         -6.14618   25.04891  -0.245   0.8063  
## promoVIP         19.85365   29.03511   0.684   0.4945  
## promoVP1200     -13.55903   32.85159  -0.413   0.6800  
## promoVPFP200     14.44690   24.75839   0.584   0.5599  
## promoWC1         26.75784   26.42159   1.013   0.3118  
## promoWild Card    6.11712   30.89824   0.198   0.8432  
## stateAL          -0.97446   25.62438  -0.038   0.9697  
## stateAR           9.38985   26.83588   0.350   0.7266  
## stateAZ           7.53285   22.48932   0.335   0.7378  
## stateCA          12.47958   21.23239   0.588   0.5570  
## stateCO           0.93859   21.89031   0.043   0.9658  
## stateCT           3.17577   22.17152   0.143   0.8862  
## stateFL          11.85637   21.37329   0.555   0.5794  
## stateGA           9.34873   21.70326   0.431   0.6669  
## stateGU          60.18126   31.99879   1.881   0.0608 .
## stateHI          -7.00034   24.51760  -0.286   0.7754  
## stateIA          12.43935   24.51708   0.507   0.6122  
## stateID           1.96774   30.18050   0.065   0.9481  
## stateIL           4.41483   21.67815   0.204   0.8387  
## stateIN           2.25104   22.87744   0.098   0.9217  
## stateKS           2.73577   22.58748   0.121   0.9037  
## stateKY           5.62282   22.29858   0.252   0.8011  
## stateLA           8.61040   25.25996   0.341   0.7334  
## stateMA           1.73441   22.62796   0.077   0.9389  
## stateMD           9.14952   23.58489   0.388   0.6983  
## stateME           0.78155   24.41827   0.032   0.9745  
## stateMI           0.48669   22.06065   0.022   0.9824  
## stateMN           1.53324   23.62358   0.065   0.9483  
## stateMO          12.16391   22.89886   0.531   0.5956  
## stateMS           5.04088   22.68813   0.222   0.8243  
## stateMT          11.10565   25.93029   0.428   0.6687  
## stateNC           3.99643   21.87168   0.183   0.8551  
## stateND           4.05635   30.63815   0.132   0.8947  
## stateNE          -3.08792   23.68299  -0.130   0.8963  
## stateNH           7.46211   24.87698   0.300   0.7644  
## stateNJ          11.35090   21.76356   0.522   0.6023  
## stateNM           0.96618   30.62577   0.032   0.9748  
## stateNV          11.06237   22.58335   0.490   0.6245  
## stateNY           8.56472   21.36350   0.401   0.6887  
## stateOH          -0.07229   22.74599  -0.003   0.9975  
## stateOK          12.64305   22.61100   0.559   0.5764  
## stateOR           6.50885   22.86981   0.285   0.7761  
## statePA          -1.51525   21.81498  -0.069   0.9447  
## statePR          16.04762   22.61323   0.710   0.4784  
## stateRI           6.57286   29.69666   0.221   0.8250  
## stateSC          -2.80658   23.99163  -0.117   0.9069  
## stateTN           9.94518   22.81704   0.436   0.6632  
## stateTX           8.18250   21.32964   0.384   0.7015  
## stateUT          -3.72114   23.49325  -0.158   0.8742  
## stateVA           1.15410   24.56771   0.047   0.9626  
## stateVT          -1.15835   29.88522  -0.039   0.9691  
## stateWA          -3.19136   23.26941  -0.137   0.8910  
## stateWI          -9.34337   29.78732  -0.314   0.7539  
## stateWV          -1.78225   31.07091  -0.057   0.9543  
## stateWY           0.56109   33.93408   0.017   0.9868  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.51 on 376 degrees of freedom
## Multiple R-squared:  0.2178, Adjusted R-squared:  -0.03802 
## F-statistic: 0.8514 on 123 and 376 DF,  p-value: 0.854

anova(lm6)

result$var[6] <- "lm(formula = Order_Qty ~ Qt + Brand + promo + state, data = lm_cust_s2)"
result$pval[6] <- "Adjusted R-squared:  0.04593 F-statistic:   1.2 on 120 and 378 DF,  p-value: 0.1016"

result$comment[6] <- "promo is very less significant now, nothing else is significant" 

#7 Drop Brand

set.seed(12123)

lm7 <- lm(Order_Qty ~  Qt + promo + state,lm_cust_s2)
summary(lm7)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + promo + state, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.064  -8.453  -1.871   3.679 275.634 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      -5.8361    29.6841  -0.197   0.8442  
## QtQ1_18          -6.8155    13.1503  -0.518   0.6045  
## QtQ2_17           2.9903     4.8709   0.614   0.5396  
## QtQ2_18          -3.2517    12.8969  -0.252   0.8011  
## QtQ3_17          -2.4078    13.0583  -0.184   0.8538  
## QtQ3_18          -9.4536    13.1759  -0.717   0.4735  
## QtQ4_17          -6.6945    12.6442  -0.529   0.5968  
## QtQ4_18          -0.3352    13.2263  -0.025   0.9798  
## promoCODE F      -2.4828    23.7023  -0.105   0.9166  
## promoH15          4.5176    21.9520   0.206   0.8371  
## promoHC18         2.2103    30.6962   0.072   0.9426  
## promoLUX40        8.9112    21.7017   0.411   0.6816  
## promoNASC150      8.8157    26.2911   0.335   0.7376  
## promoNASC75      -1.7234    31.0307  -0.056   0.9557  
## promoNB           9.3594    30.2236   0.310   0.7570  
## promoNB40        20.5520    30.0894   0.683   0.4950  
## promoOO15         3.2297    31.8710   0.101   0.9193  
## promoOOX40       27.2252    26.2994   1.035   0.3012  
## promoOther       14.2439    24.9554   0.571   0.5685  
## promoOY12        14.4652    30.5713   0.473   0.6364  
## promoPB3          1.4279    30.0617   0.047   0.9621  
## promoPRE-SELL T   2.7075    30.4716   0.089   0.9292  
## promoPRE-SELL V  24.2461    36.9827   0.656   0.5124  
## promoPRE SELL T   5.3817    30.8016   0.175   0.8614  
## promoRB15        25.7572    26.3920   0.976   0.3297  
## promoRSD         38.3215    32.5861   1.176   0.2403  
## promoSUN1        51.4376    30.5036   1.686   0.0925 .
## promoSY1         13.5194    25.3683   0.533   0.5944  
## promoSY100       11.0945    25.1804   0.441   0.6597  
## promoSY1000       6.8399    27.8822   0.245   0.8063  
## promoSY2          8.9155    26.9312   0.331   0.7408  
## promoSY200       12.7831    23.6287   0.541   0.5888  
## promoSY250       24.1831    25.7689   0.938   0.3486  
## promoSY5         13.3775    27.0189   0.495   0.6208  
## promoSYNERGY54    6.5813    26.5173   0.248   0.8041  
## promoSYVE        25.3445    26.3357   0.962   0.3364  
## promoUP1          5.3629    21.8511   0.245   0.8062  
## promoUP3          1.6612    22.3605   0.074   0.9408  
## promoVIP         28.6234    26.4531   1.082   0.2799  
## promoVP1200      -0.9022    30.7409  -0.029   0.9766  
## promoVPFP200     19.8060    23.2491   0.852   0.3948  
## promoWC1         31.3040    23.9135   1.309   0.1913  
## promoWild Card    9.0270    27.9390   0.323   0.7468  
## stateAL           5.7039    25.3243   0.225   0.8219  
## stateAR          16.3473    25.4957   0.641   0.5218  
## stateAZ          10.4641    22.1373   0.473   0.6367  
## stateCA          16.2938    20.9567   0.778   0.4373  
## stateCO           7.4082    21.5097   0.344   0.7307  
## stateCT           7.3483    21.7572   0.338   0.7357  
## stateFL          13.4864    21.1499   0.638   0.5241  
## stateGA          13.8361    21.3742   0.647   0.5178  
## stateGU          73.7475    31.5818   2.335   0.0200 *
## stateHI           2.1359    23.9752   0.089   0.9291  
## stateIA          22.7525    24.2334   0.939   0.3483  
## stateID          14.8440    29.4220   0.505   0.6142  
## stateIL           8.2861    21.3532   0.388   0.6982  
## stateIN           6.9454    22.3788   0.310   0.7564  
## stateKS           9.1286    22.1756   0.412   0.6808  
## stateKY           4.6355    22.0256   0.210   0.8334  
## stateLA           4.7482    24.1050   0.197   0.8439  
## stateMA           6.3419    22.3157   0.284   0.7764  
## stateMD          13.5545    23.2315   0.583   0.5599  
## stateME           2.9414    24.1003   0.122   0.9029  
## stateMI           4.9335    21.5874   0.229   0.8193  
## stateMN           5.2760    23.2849   0.227   0.8209  
## stateMO          12.0141    22.5223   0.533   0.5940  
## stateMS           7.0995    22.3247   0.318   0.7506  
## stateMT           8.2268    25.5198   0.322   0.7473  
## stateNC           5.4109    21.5368   0.251   0.8018  
## stateND           4.4362    29.8414   0.149   0.8819  
## stateNE           5.3056    23.3057   0.228   0.8200  
## stateNH          14.8982    23.9116   0.623   0.5336  
## stateNJ          14.4608    21.5010   0.673   0.5016  
## stateNM           9.1749    30.3381   0.302   0.7625  
## stateNV          13.5692    22.3122   0.608   0.5434  
## stateNY          10.7664    21.0482   0.512   0.6093  
## stateOH           3.3710    22.2115   0.152   0.8794  
## stateOK          14.5818    22.1722   0.658   0.5111  
## stateOR           7.0323    22.5228   0.312   0.7550  
## statePA           2.7267    21.5007   0.127   0.8991  
## statePR          16.7383    22.4576   0.745   0.4565  
## stateRI          12.8440    29.4220   0.437   0.6627  
## stateSC           3.6161    23.3850   0.155   0.8772  
## stateTN          12.8652    22.4051   0.574   0.5661  
## stateTX          10.8475    21.1097   0.514   0.6076  
## stateUT           1.8271    23.3345   0.078   0.9376  
## stateVA           1.9079    24.2370   0.079   0.9373  
## stateVT          10.0000    29.1305   0.343   0.7316  
## stateWA          -1.7696    22.8754  -0.077   0.9384  
## stateWI          -1.0726    29.4932  -0.036   0.9710  
## stateWV           1.5901    30.4667   0.052   0.9584  
## stateWY          -4.1560    29.4220  -0.141   0.8877  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.6 on 408 degrees of freedom
## Multiple R-squared:  0.1441, Adjusted R-squared:  -0.04684 
## F-statistic: 0.7547 on 91 and 408 DF,  p-value: 0.9483

anova(lm7)

result$var[7] <- "lm(formula = Order_Qty ~ Qt + promo + state, data = lm_cust_s2)"
result$pval[7] <- "Adjusted R-squared:  0.04285 F-statistic: 1.251 on 89 and 409 DF,  p-value: 0.07818"

result$comment[7] <- "not much. sig " 



#8 Drop state and Brand

set.seed(12126)

lm8 <- lm(Order_Qty ~    Qt + promo + Brand,lm_cust_s2)
summary(lm8)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + promo + Brand, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -25.499  -8.105  -1.961   3.530 275.230 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)
## (Intercept)      15.63730   25.68654   0.609    0.543
## QtQ1_18          -0.58682   12.29368  -0.048    0.962
## QtQ2_17          -2.17451    4.70740  -0.462    0.644
## QtQ2_18           4.60028   12.02397   0.383    0.702
## QtQ3_17           3.34840   12.09371   0.277    0.782
## QtQ3_18          -1.50272   12.23675  -0.123    0.902
## QtQ4_17          -0.16126   11.65991  -0.014    0.989
## QtQ4_18           4.47973   12.31442   0.364    0.716
## promoCODE F      -5.95422   25.20613  -0.236    0.813
## promoH15          0.04934   23.35115   0.002    0.998
## promoHC18        -0.77270   34.16125  -0.023    0.982
## promoLUX40        8.38598   23.08882   0.363    0.717
## promoNASC150     12.91374   27.69123   0.466    0.641
## promoNASC75       1.12986   31.22372   0.036    0.971
## promoNB           6.12749   30.66514   0.200    0.842
## promoNB40        26.49368   30.80911   0.860    0.390
## promoOO15        -9.87251   30.66514  -0.322    0.748
## promoOOX40       14.03684   27.26014   0.515    0.607
## promoOther        1.02133   25.57811   0.040    0.968
## promoOY12         2.72967   30.61166   0.089    0.929
## promoPB3          5.26925   32.43063   0.162    0.871
## promoPRE-SELL T  -2.01869   30.81789  -0.066    0.948
## promoPRE-SELL V  12.24363   33.41101   0.366    0.714
## promoPRE SELL T   7.15582   31.18429   0.229    0.819
## promoRB15        17.12749   27.19421   0.630    0.529
## promoRSD         21.33846   32.76436   0.651    0.515
## promoSUN1        42.12749   30.66514   1.374    0.170
## promoSY1          4.12327   26.04488   0.158    0.874
## promoSY100        4.05058   25.72637   0.157    0.875
## promoSY1000       2.09977   28.37520   0.074    0.941
## promoSY2         -0.73703   27.33003  -0.027    0.978
## promoSY200       18.16933   24.83652   0.732    0.465
## promoSY250       15.09253   26.24829   0.575    0.566
## promoSY5          5.61552   27.31580   0.206    0.837
## promoSYNERGY54   -7.42698   26.25011  -0.283    0.777
## promoSYVE        11.95307   26.92468   0.444    0.657
## promoUP1          3.68509   23.19796   0.159    0.874
## promoUP3         -3.39548   23.77836  -0.143    0.887
## promoVIP         15.77279   27.44812   0.575    0.566
## promoVP1200      -4.06126   30.46462  -0.133    0.894
## promoVPFP200     16.80703   23.52874   0.714    0.475
## promoWC1         23.86248   24.97679   0.955    0.340
## promoWild Card    3.32694   28.99871   0.115    0.909
## BrandAX         -10.04663   14.16467  -0.709    0.479
## BrandBB          -8.69009   19.17740  -0.453    0.651
## BrandBE          -5.59265   13.47393  -0.415    0.678
## BrandBV         -15.26682   18.75551  -0.814    0.416
## BrandCH          -7.63730   16.06693  -0.475    0.635
## BrandDG         -12.67108   13.58884  -0.932    0.352
## BrandDY          -8.29197   18.96041  -0.437    0.662
## BrandEA           4.40891   15.25730   0.289    0.773
## BrandHC          -1.57604   12.74416  -0.124    0.902
## BrandMK          -5.15996   13.09671  -0.394    0.694
## BrandMU         -12.17703   15.75989  -0.773    0.440
## BrandOJ         -17.90655   16.95110  -1.056    0.291
## BrandOO           3.63116   12.71348   0.286    0.775
## BrandOX           1.91312   13.11540   0.146    0.884
## BrandOY          -6.36696   13.10011  -0.486    0.627
## BrandPH         -11.91577   12.95562  -0.920    0.358
## BrandPO          -1.33503   17.23805  -0.077    0.938
## BrandPP         -11.41569   15.91653  -0.717    0.474
## BrandPR          -5.95648   12.61475  -0.472    0.637
## BrandPS         -16.53955   14.20647  -1.164    0.245
## BrandRA         -15.20685   19.87971  -0.765    0.445
## BrandRB           0.40972   12.38283   0.033    0.974
## BrandRJ         -15.27484   14.75218  -1.035    0.301
## BrandRL         -16.03844   14.68319  -1.092    0.275
## BrandRX          -3.91831   12.37546  -0.317    0.752
## BrandRY         -14.33431   12.45980  -1.150    0.251
## BrandSF         -16.16536   18.74040  -0.863    0.389
## BrandTF          -7.61861   13.35475  -0.570    0.569
## BrandTY         -14.60137   13.73456  -1.063    0.288
## BrandVA          -7.88093   19.11869  -0.412    0.680
## BrandVE          -7.49532   13.10598  -0.572    0.568
## BrandVO          -7.62982   13.48761  -0.566    0.572
## 
## Residual standard error: 20.04 on 425 degrees of freedom
## Multiple R-squared:  0.156,  Adjusted R-squared:  0.009023 
## F-statistic: 1.061 on 74 and 425 DF,  p-value: 0.3527

anova(lm8)

result$var[8] <- "lm(formula = Order_Qty ~ Qt + promo + Brand, data = lm_cust_s2)"
result$pval[8] <- "Adjusted R-squared:  0.04555 F-statistic:  1.34 on 70 and 429 DF,  p-value: 0.04416"
result$comment[8] <- "not much sig." 


lm9 <- lm(formula = Order_Qty ~ Qt + Brand + promo + month, data = lm_cust_s2)  
summary(lm9)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + Brand + promo + month, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.848  -8.309  -1.492   3.727 267.585 
## 
## Coefficients: (3 not defined because of singularities)
##                 Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      25.4685    26.1218   0.975   0.3301  
## QtQ1_18          -5.6092    12.4000  -0.452   0.6513  
## QtQ2_17         -10.9398     6.2077  -1.762   0.0787 .
## QtQ2_18          -8.1666    12.9309  -0.632   0.5280  
## QtQ3_17          -4.3543    12.8939  -0.338   0.7358  
## QtQ3_18          -9.4580    13.1511  -0.719   0.4724  
## QtQ4_17         -12.8841    13.0152  -0.990   0.3228  
## QtQ4_18          -5.8497    13.3477  -0.438   0.6614  
## BrandAX          -9.4196    14.2668  -0.660   0.5095  
## BrandBB          -5.9477    19.2645  -0.309   0.7577  
## BrandBE          -5.6269    13.5310  -0.416   0.6777  
## BrandBV         -18.2668    18.8627  -0.968   0.3334  
## BrandCH          -9.7403    16.1615  -0.603   0.5470  
## BrandDG         -12.0797    13.6682  -0.884   0.3773  
## BrandDY          -3.4774    19.0779  -0.182   0.8555  
## BrandEA           4.2133    15.2976   0.275   0.7831  
## BrandHC          -2.0489    12.7963  -0.160   0.8729  
## BrandMK          -5.1656    13.1435  -0.393   0.6945  
## BrandMU         -11.2197    15.7994  -0.710   0.4780  
## BrandOJ         -18.8207    16.9621  -1.110   0.2678  
## BrandOO           3.8081    12.7939   0.298   0.7661  
## BrandOX           2.5956    13.1523   0.197   0.8436  
## BrandOY          -5.7431    13.1197  -0.438   0.6618  
## BrandPH         -11.2629    12.9928  -0.867   0.3865  
## BrandPO          -1.1515    17.2574  -0.067   0.9468  
## BrandPP          -9.4005    16.1514  -0.582   0.5609  
## BrandPR          -7.2997    12.6564  -0.577   0.5644  
## BrandPS         -17.9144    14.2381  -1.258   0.2090  
## BrandRA         -13.4667    20.0193  -0.673   0.5015  
## BrandRB           0.1095    12.4167   0.009   0.9930  
## BrandRJ         -13.2835    14.8080  -0.897   0.3702  
## BrandRL         -15.4852    14.7574  -1.049   0.2946  
## BrandRX          -4.2402    12.4251  -0.341   0.7331  
## BrandRY         -14.6180    12.5106  -1.168   0.2433  
## BrandSF         -16.2623    18.8171  -0.864   0.3880  
## BrandTF          -7.1494    13.3948  -0.534   0.5938  
## BrandTY         -13.2043    13.7958  -0.957   0.3391  
## BrandVA          -4.2358    19.1546  -0.221   0.8251  
## BrandVE          -7.7708    13.1376  -0.591   0.5545  
## BrandVO          -7.0594    13.5342  -0.522   0.6022  
## promoCODE F     -12.4659    25.3217  -0.492   0.6228  
## promoH15         -6.8867    23.4434  -0.294   0.7691  
## promoHC18       -10.8878    34.5514  -0.315   0.7528  
## promoLUX40        2.8168    23.1718   0.122   0.9033  
## promoNASC150      2.7370    27.8081   0.098   0.9216  
## promoNASC75      -8.7704    31.3382  -0.280   0.7797  
## promoNB          -0.9450    30.9199  -0.031   0.9756  
## promoNB40        20.4642    31.0706   0.659   0.5105  
## promoOO15       -10.6382    30.7639  -0.346   0.7297  
## promoOOX40        9.6565    27.4174   0.352   0.7249  
## promoOther        0.1816    25.6711   0.007   0.9944  
## promoOY12        -7.7255    30.9532  -0.250   0.8030  
## promoPB3         -3.6479    32.7594  -0.111   0.9114  
## promoPRE-SELL T  -4.5909    30.7320  -0.149   0.8813  
## promoPRE-SELL V   6.4955    33.3576   0.195   0.8457  
## promoPRE SELL T  -0.6861    31.4486  -0.022   0.9826  
## promoRB15        13.2084    27.3305   0.483   0.6291  
## promoRSD         18.4402    33.0220   0.558   0.5769  
## promoSUN1        35.0550    30.9199   1.134   0.2576  
## promoSY1          1.2098    26.1433   0.046   0.9631  
## promoSY100        2.8471    25.8205   0.110   0.9123  
## promoSY1000       2.7455    28.5773   0.096   0.9235  
## promoSY2         -5.0276    27.4162  -0.183   0.8546  
## promoSY200       14.2891    24.9980   0.572   0.5679  
## promoSY250       13.9756    26.4013   0.529   0.5968  
## promoSY5          4.5020    27.5171   0.164   0.8701  
## promoSYNERGY54   -9.8122    26.3440  -0.372   0.7097  
## promoSYVE        10.3155    27.0718   0.381   0.7034  
## promoUP1         -3.0098    23.3087  -0.129   0.8973  
## promoUP3         -9.6455    23.9144  -0.403   0.6869  
## promoVIP         17.4621    27.6093   0.632   0.5274  
## promoVP1200     -13.4196    30.7206  -0.437   0.6625  
## promoVPFP200     10.8929    23.9499   0.455   0.6495  
## promoWC1         20.8624    25.0744   0.832   0.4059  
## promoWild Card    1.8410    29.1719   0.063   0.9497  
## month2           -7.7282     4.8906  -1.580   0.1148  
## month3           -3.5016     5.0938  -0.687   0.4922  
## month4            8.8686     4.7010   1.887   0.0599 .
## month5            6.3068     4.5112   1.398   0.1628  
## month6                NA         NA      NA       NA  
## month7           -2.0712     5.5160  -0.375   0.7075  
## month8           -1.4940     4.0877  -0.365   0.7149  
## month9                NA         NA      NA       NA  
## month10          -0.6478     5.0822  -0.127   0.8986  
## month11           8.8062     4.9822   1.768   0.0779 .
## month12               NA         NA      NA       NA  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.96 on 417 degrees of freedom
## Multiple R-squared:  0.1786, Adjusted R-squared:  0.01712 
## F-statistic: 1.106 on 82 and 417 DF,  p-value: 0.2631

anova(lm9)

result$var[9] <- "lm(formula = Order_Qty ~ Qt + Brand + promo + month, data = lm_cust_s2)"
result$pval[9] <- "Adjusted R-squared:  0.05115 F-statistic: 1.345 on 78 and 421 DF,  p-value: 0.03633"
result$comment[9] <- "Pvalue looks less than  to .05"

lm10 <- lm(formula = Order_Qty ~ Qt + promo + month, data = lm_cust_s2)
summary(lm10)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + promo + month, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -31.892  -8.505  -2.770   3.470 275.180 
## 
## Coefficients: (3 not defined because of singularities)
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      15.29416   20.61528   0.742   0.4585  
## QtQ1_18          -5.52179   11.94717  -0.462   0.6442  
## QtQ2_17          -9.29586    5.95698  -1.560   0.1193  
## QtQ2_18         -10.62355   12.44912  -0.853   0.3939  
## QtQ3_17          -5.27074   12.52031  -0.421   0.6740  
## QtQ3_18         -12.13249   12.64870  -0.959   0.3380  
## QtQ4_17         -12.52851   12.52000  -1.001   0.3175  
## QtQ4_18          -5.19040   12.88812  -0.403   0.6873  
## promoCODE F      -5.21900   22.89544  -0.228   0.8198  
## promoH15         -1.72497   20.99034  -0.082   0.9345  
## promoHC18        -9.99558   29.01323  -0.345   0.7306  
## promoLUX40        6.06913   20.69518   0.293   0.7695  
## promoNASC150      4.38215   25.26473   0.173   0.8624  
## promoNASC75      -6.11785   28.97415  -0.211   0.8329  
## promoNB           6.00442   29.01323   0.207   0.8361  
## promoNB40        20.00442   29.01323   0.689   0.4909  
## promoOO15        -1.99830   28.95670  -0.069   0.9450  
## promoOOX40       22.61872   24.95844   0.906   0.3653  
## promoOther        5.93621   23.31379   0.255   0.7991  
## promoOY12        -3.29416   28.76421  -0.115   0.9089  
## promoPB3        -12.29416   28.76421  -0.427   0.6693  
## promoPRE-SELL T  -2.00000   28.36864  -0.071   0.9438  
## promoPRE-SELL V  12.00000   28.36864   0.423   0.6725  
## promoPRE SELL T  -0.99558   29.01323  -0.034   0.9726  
## promoRB15        21.00306   25.18059   0.834   0.4047  
## promoRSD         27.33211   30.95101   0.883   0.3777  
## promoSUN1        42.00442   29.01323   1.448   0.1484  
## promoSY1          4.69157   23.68312   0.198   0.8431  
## promoSY100        4.63037   23.50161   0.197   0.8439  
## promoSY1000       5.01228   26.28522   0.191   0.8489  
## promoSY2         -1.40579   25.13091  -0.056   0.9554  
## promoSY200       17.05300   22.48596   0.758   0.4486  
## promoSY250       18.07762   24.12589   0.749   0.4541  
## promoSY5          6.74014   25.26120   0.267   0.7897  
## promoSYNERGY54   -3.12684   24.55611  -0.127   0.8987  
## promoSYVE        16.89315   24.74080   0.683   0.4951  
## promoUP1         -0.09184   20.84021  -0.004   0.9965  
## promoUP3         -3.15163   21.41517  -0.147   0.8831  
## promoVIP         25.72993   25.09768   1.025   0.3058  
## promoVP1200      -5.29416   28.76421  -0.184   0.8541  
## promoVPFP200     17.03574   22.45344   0.759   0.4484  
## promoWC1         24.34589   22.61936   1.076   0.2824  
## promoWild Card    4.50231   26.20562   0.172   0.8637  
## month2           -7.29416    4.75394  -1.534   0.1257  
## month3           -5.52990    4.87257  -1.135   0.2570  
## month4            9.11955    4.58482   1.989   0.0473 *
## month5            7.99728    4.41454   1.812   0.0707 .
## month6                 NA         NA      NA       NA  
## month7           -0.14539    5.34835  -0.027   0.9783  
## month8            0.61627    3.94551   0.156   0.8759  
## month9                 NA         NA      NA       NA  
## month10          -1.83139    4.93105  -0.371   0.7105  
## month11           8.78052    4.79840   1.830   0.0679 .
## month12                NA         NA      NA       NA  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.06 on 449 degrees of freedom
## Multiple R-squared:  0.1067, Adjusted R-squared:  0.007203 
## F-statistic: 1.072 on 50 and 449 DF,  p-value: 0.3482

anova(lm10)

result$var[10] <- "lm(formula = Order_Qty ~ Qt + promo + month, data = lm_cust_s2)"
result$pval[10] <- "Adjusted R-squared:  0.0448 
F-statistic: 1.498 on 47 and 452 DF,  p-value: 0.02147"
result$comment[10] <- "not much sig."


# p-value: 0.02331
lm_pbm <- lm(formula = Order_Qty ~  promo + Brand + month, data = lm_cust_s2)

summary(lm(formula = Order_Qty ~  promo + Brand + month, data = lm_cust_s2))

## 
## Call:
## lm(formula = Order_Qty ~ promo + Brand + month, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.914  -8.133  -1.654   3.478 272.944 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)
## (Intercept)      26.13481   26.10286   1.001    0.317
## promoCODE F     -15.96890   25.23730  -0.633    0.527
## promoH15         -8.72719   23.45000  -0.372    0.710
## promoHC18       -19.24662   34.26227  -0.562    0.575
## promoLUX40        0.65737   23.17376   0.028    0.977
## promoNASC150     -1.28252   27.65930  -0.046    0.963
## promoNASC75     -14.85914   31.18716  -0.476    0.634
## promoNB          -6.14625   30.76470  -0.200    0.842
## promoNB40        15.07273   30.93316   0.487    0.626
## promoOO15       -16.15442   30.59427  -0.528    0.598
## promoOOX40        6.81802   27.41124   0.249    0.804
## promoOther       -3.73615   22.87707  -0.163    0.870
## promoOY12        -7.04911   31.00791  -0.227    0.820
## promoPB3         -6.01193   32.81257  -0.183    0.855
## promoPRE-SELL T  -4.13293   30.79075  -0.134    0.893
## promoPRE-SELL V   7.67132   33.41142   0.230    0.819
## promoPRE SELL T  -5.42158   31.26403  -0.173    0.862
## promoRB15         7.84967   27.13088   0.289    0.772
## promoRSD         16.07839   30.92792   0.520    0.603
## promoSUN1        29.85375   30.76470   0.970    0.332
## promoSY1          0.03163   23.35211   0.001    0.999
## promoSY100       -0.56330   23.22642  -0.024    0.981
## promoSY1000      -3.43163   25.67911  -0.134    0.894
## promoSY2         -4.81010   24.79152  -0.194    0.846
## promoSY200        8.62250   24.36471   0.354    0.724
## promoSY250        8.06814   23.49242   0.343    0.731
## promoSY5          3.93312   24.81882   0.158    0.874
## promoSYNERGY54   -9.85176   23.61471  -0.417    0.677
## promoSYVE         3.35126   24.29424   0.138    0.890
## promoUP1         -5.59888   23.29931  -0.240    0.810
## promoUP3        -13.01644   23.86255  -0.545    0.586
## promoVIP         14.93715   24.92897   0.599    0.549
## promoVP1200     -13.31577   30.77976  -0.433    0.666
## promoVPFP200     10.07814   23.99677   0.420    0.675
## promoWC1         17.74550   24.22135   0.733    0.464
## promoWild Card   -4.61956   26.46511  -0.175    0.862
## BrandAX         -10.95095   13.99807  -0.782    0.434
## BrandBB          -3.49403   19.13093  -0.183    0.855
## BrandBE          -4.82203   13.43485  -0.359    0.720
## BrandBV         -19.33190   18.85157  -1.025    0.306
## BrandCH         -10.45199   16.05497  -0.651    0.515
## BrandDG         -13.11649   13.48968  -0.972    0.331
## BrandDY          -6.86874   18.90344  -0.363    0.717
## BrandEA           4.50472   15.22928   0.296    0.768
## BrandHC          -2.81904   12.67625  -0.222    0.824
## BrandMK          -5.46062   13.01448  -0.420    0.675
## BrandMU         -12.97826   15.65353  -0.829    0.408
## BrandOJ         -17.12288   16.84112  -1.017    0.310
## BrandOO           2.50665   12.69621   0.197    0.844
## BrandOX           1.61952   13.06314   0.124    0.901
## BrandOY          -7.08570   12.97111  -0.546    0.585
## BrandPH         -11.87732   12.88164  -0.922    0.357
## BrandPO          -3.96044   17.19708  -0.230    0.818
## BrandPP         -13.70844   16.01366  -0.856    0.392
## BrandPR          -7.81338   12.60822  -0.620    0.536
## BrandPS         -17.09130   14.11834  -1.211    0.227
## BrandRA         -12.97364   19.96227  -0.650    0.516
## BrandRB          -0.59440   12.28941  -0.048    0.961
## BrandRJ         -15.00836   14.67000  -1.023    0.307
## BrandRL         -16.06863   14.66091  -1.096    0.274
## BrandRX          -4.88683   12.30268  -0.397    0.691
## BrandRY         -15.63530   12.40539  -1.260    0.208
## BrandSF         -17.20566   18.74432  -0.918    0.359
## BrandTF          -8.31906   13.32859  -0.624    0.533
## BrandTY         -14.79733   13.57891  -1.090    0.276
## BrandVA          -6.12332   19.06459  -0.321    0.748
## BrandVE          -8.31584   13.04585  -0.637    0.524
## BrandVO          -7.93330   13.45593  -0.590    0.556
## month2           -7.68282    4.89698  -1.569    0.117
## month3           -2.75872    5.08822  -0.542    0.588
## month4            2.54636    5.16142   0.493    0.622
## month5            0.60584    5.21460   0.116    0.908
## month6           -5.38599    4.82769  -1.116    0.265
## month7           -4.68335    6.21103  -0.754    0.451
## month8           -4.48277    4.89863  -0.915    0.361
## month9           -2.45666    5.05541  -0.486    0.627
## month10          -5.75226    5.33533  -1.078    0.282
## month11           2.15030    5.31743   0.404    0.686
## month12          -4.84616    5.42623  -0.893    0.372
## 
## Residual standard error: 20 on 421 degrees of freedom
## Multiple R-squared:  0.1672, Adjusted R-squared:  0.01286 
## F-statistic: 1.083 on 78 and 421 DF,  p-value: 0.3076

anova(lm(formula = Order_Qty ~  promo + Brand + month, data = lm_cust_s2))

# p-value: 0.0177
lm_pd <- lm(formula = Order_Qty ~  promo  + `Order Date`, data = lm_cust_s2)
anova(lm(formula = Order_Qty ~  promo  + `Order Date`, data = lm_cust_s2))

summary(lm(formula = Order_Qty ~  promo  + `Order Date`, data = lm_cust_s2))

## 
## Call:
## lm(formula = Order_Qty ~ promo + `Order Date`, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.953  -8.500  -3.518   2.919 287.524 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      7.481e+01  1.359e+02   0.551   0.5822  
## promoCODE F     -1.667e+00  2.255e+01  -0.074   0.9411  
## promoH15         2.146e+00  2.083e+01   0.103   0.9180  
## promoHC18       -3.616e+00  2.853e+01  -0.127   0.8992  
## promoLUX40       9.065e+00  2.057e+01   0.441   0.6596  
## promoNASC150     1.178e+01  2.470e+01   0.477   0.6338  
## promoNASC75      1.268e+00  2.852e+01   0.044   0.9646  
## promoNB          1.238e+01  2.853e+01   0.434   0.6646  
## promoNB40        2.641e+01  2.853e+01   0.926   0.3550  
## promoOO15       -3.515e+00  2.853e+01  -0.123   0.9020  
## promoOOX40       2.281e+01  2.470e+01   0.923   0.3562  
## promoOther       6.914e+00  2.047e+01   0.338   0.7357  
## promoOY12        3.860e+00  2.852e+01   0.135   0.8924  
## promoPB3        -5.101e+00  2.852e+01  -0.179   0.8581  
## promoPRE-SELL T -2.047e+00  2.852e+01  -0.072   0.9428  
## promoPRE-SELL V  1.198e+01  2.852e+01   0.420   0.6746  
## promoPRE SELL T  5.342e+00  2.853e+01   0.187   0.8515  
## promoRB15        2.342e+01  2.471e+01   0.948   0.3438  
## promoRSD         3.372e+01  2.873e+01   1.174   0.2410  
## promoSUN1        4.838e+01  2.853e+01   1.696   0.0906 .
## promoSY1         1.127e+01  2.101e+01   0.536   0.5921  
## promoSY100       6.722e+00  2.049e+01   0.328   0.7430  
## promoSY1000      2.193e+00  2.349e+01   0.093   0.9256  
## promoSY2         8.096e+00  2.265e+01   0.357   0.7210  
## promoSY200       1.927e+01  2.160e+01   0.892   0.3728  
## promoSY250       1.669e+01  2.106e+01   0.792   0.4286  
## promoSY5         1.317e+01  2.269e+01   0.581   0.5618  
## promoSYNERGY54   3.545e+00  2.193e+01   0.162   0.8717  
## promoSYVE        1.438e+01  2.202e+01   0.653   0.5140  
## promoUP1         4.190e+00  2.064e+01   0.203   0.8392  
## promoUP3        -1.562e-01  2.115e+01  -0.007   0.9941  
## promoVIP         2.588e+01  2.241e+01   1.155   0.2488  
## promoVP1200      1.918e+00  2.852e+01   0.067   0.9464  
## promoVPFP200     1.891e+01  2.209e+01   0.856   0.3925  
## promoWC1         2.599e+01  2.162e+01   1.202   0.2300  
## promoWild Card   3.443e+00  2.346e+01   0.147   0.8834  
## `Order Date`    -4.493e-08  9.036e-08  -0.497   0.6193  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.16 on 463 degrees of freedom
## Multiple R-squared:  0.06917,    Adjusted R-squared:  -0.003208 
## F-statistic: 0.9557 on 36 and 463 DF,  p-value: 0.5453

#p-value: 0.0169
lm_py <- lm(formula = Order_Qty ~  promo  + year(`Order Date`), data = lm_cust_s2)
summary(lm(formula = Order_Qty ~  promo  + year(`Order Date`), data = lm_cust_s2))

## 
## Call:
## lm(formula = Order_Qty ~ promo + year(`Order Date`), data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.536  -8.282  -3.282   2.952 287.093 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)  
## (Intercept)        2781.638   5517.284   0.504    0.614  
## promoCODE F          -2.000     22.544  -0.089    0.929  
## promoH15              2.000     20.826   0.096    0.924  
## promoHC18            -4.000     28.517  -0.140    0.889  
## promoLUX40            8.920     20.564   0.434    0.665  
## promoNASC150         11.500     24.696   0.466    0.642  
## promoNASC75           1.000     28.517   0.035    0.972  
## promoNB              12.000     28.517   0.421    0.674  
## promoNB40            26.000     28.517   0.912    0.362  
## promoOO15            -4.000     28.517  -0.140    0.889  
## promoOOX40           22.500     24.696   0.911    0.363  
## promoOther            6.282     20.303   0.309    0.757  
## promoOY12             4.000     28.517   0.140    0.889  
## promoPB3             -5.000     28.517  -0.175    0.861  
## promoPRE-SELL T      -2.000     28.517  -0.070    0.944  
## promoPRE-SELL V      12.000     28.517   0.421    0.674  
## promoPRE SELL T       5.000     28.517   0.175    0.861  
## promoRB15            23.000     24.696   0.931    0.352  
## promoRSD             33.375     28.648   1.165    0.245  
## promoSUN1            48.000     28.517   1.683    0.093 .
## promoSY1             10.495     20.745   0.506    0.613  
## promoSY100            5.872     20.421   0.288    0.774  
## promoSY1000           2.042     23.444   0.087    0.931  
## promoSY2              6.975     22.258   0.313    0.754  
## promoSY200           18.571     21.557   0.862    0.389  
## promoSY250           16.563     21.026   0.788    0.431  
## promoSY5             11.975     22.258   0.538    0.591  
## promoSYNERGY54        2.500     21.562   0.116    0.908  
## promoSYVE            13.518     21.730   0.622    0.534  
## promoUP1              4.048     20.639   0.196    0.845  
## promoUP3             -0.400     21.149  -0.019    0.985  
## promoVIP             25.375     22.258   1.140    0.255  
## promoVP1200           2.000     28.517   0.070    0.944  
## promoVPFP200         18.800     22.089   0.851    0.395  
## promoWC1             25.536     21.571   1.184    0.237  
## promoWild Card        3.375     23.444   0.144    0.886  
## year(`Order Date`)   -1.375      2.735  -0.503    0.615  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.16 on 463 degrees of freedom
## Multiple R-squared:  0.06918,    Adjusted R-squared:  -0.003196 
## F-statistic: 0.9558 on 36 and 463 DF,  p-value: 0.545

anova(lm(formula = Order_Qty ~  promo  + year(`Order Date`), data = lm_cust_s2))

#p-value: 0.4186  Not considering 
summary(lm(formula = Order_Qty ~  month + Brand + Qt , data = lm_cust_s2))

## 
## Call:
## lm(formula = Order_Qty ~ month + Brand + Qt, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.498  -8.874  -2.655   3.204 269.982 
## 
## Coefficients: (3 not defined because of singularities)
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  29.1269    12.3428   2.360   0.0187 *
## month2       -6.7943     4.6972  -1.446   0.1487  
## month3       -0.9387     4.6792  -0.201   0.8411  
## month4        0.5612     5.4616   0.103   0.9182  
## month5        3.1061     5.3118   0.585   0.5590  
## month6       -4.1376     5.0463  -0.820   0.4127  
## month7       -8.9181     6.4702  -1.378   0.1688  
## month8       -8.4441     5.2204  -1.618   0.1065  
## month9       -6.2577     5.2956  -1.182   0.2380  
## month10      -6.8754     5.3708  -1.280   0.2011  
## month11       3.6261     5.5185   0.657   0.5115  
## month12      -4.4138     5.3924  -0.819   0.4135  
## BrandAX     -12.6489    13.7450  -0.920   0.3579  
## BrandBB     -18.4439    16.5445  -1.115   0.2655  
## BrandBE      -9.4183    12.8866  -0.731   0.4652  
## BrandBV     -23.8384    18.4544  -1.292   0.1971  
## BrandCH     -15.4379    14.7833  -1.044   0.2969  
## BrandDG     -17.1604    13.0550  -1.314   0.1894  
## BrandDY     -13.9609    18.4087  -0.758   0.4486  
## BrandEA      -1.5132    14.7023  -0.103   0.9181  
## BrandHC      -6.3924    12.1845  -0.525   0.6001  
## BrandMK     -10.5573    12.5645  -0.840   0.4012  
## BrandMU     -16.3056    14.7329  -1.107   0.2690  
## BrandOJ     -24.5637    15.4420  -1.591   0.1124  
## BrandOO      -2.7353    12.2287  -0.224   0.8231  
## BrandOX      -4.3621    12.4842  -0.349   0.7269  
## BrandOY     -11.9135    12.4962  -0.953   0.3409  
## BrandPH     -15.2351    12.5483  -1.214   0.2253  
## BrandPO      -2.6429    16.5329  -0.160   0.8731  
## BrandPP     -18.7140    15.6163  -1.198   0.2314  
## BrandPR     -11.2298    12.1845  -0.922   0.3572  
## BrandPS     -21.2990    13.6998  -1.555   0.1207  
## BrandRA     -18.1680    18.4453  -0.985   0.3252  
## BrandRB      -5.1201    11.8603  -0.432   0.6662  
## BrandRJ     -21.5862    14.2457  -1.515   0.1304  
## BrandRL     -21.3110    14.2458  -1.496   0.1354  
## BrandRX      -9.4992    11.8849  -0.799   0.4246  
## BrandRY     -20.0697    12.0798  -1.661   0.0973 .
## BrandSF     -23.3317    18.4149  -1.267   0.2058  
## BrandTF     -10.0557    12.8368  -0.783   0.4338  
## BrandTY     -15.4669    13.1312  -1.178   0.2395  
## BrandVA     -10.4880    16.5855  -0.632   0.5275  
## BrandVE     -11.9909    12.6397  -0.949   0.3433  
## BrandVO      -9.4192    13.0550  -0.722   0.4710  
## QtQ1_18      -2.4528     3.7735  -0.650   0.5160  
## QtQ2_17      -3.9472     3.6872  -1.071   0.2850  
## QtQ2_18           NA         NA      NA       NA  
## QtQ3_17       4.5871     3.6216   1.267   0.2060  
## QtQ3_18           NA         NA      NA       NA  
## QtQ4_17      -3.5326     4.0255  -0.878   0.3807  
## QtQ4_18           NA         NA      NA       NA  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.96 on 452 degrees of freedom
## Multiple R-squared:  0.1095, Adjusted R-squared:  0.01689 
## F-statistic: 1.182 on 47 and 452 DF,  p-value: 0.1983

#p-value: 0.0569
lm_pbms <- lm(formula = Order_Qty ~  Brand + promo + month + state,   data = lm_cust_s2)

summary(lm(formula = Order_Qty ~  Brand + promo + month + state,   data = lm_cust_s2))

## 
## Call:
## lm(formula = Order_Qty ~ Brand + promo + month + state, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -32.491  -7.112  -1.416   4.217 266.166 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)
## (Intercept)      24.34140   34.65968   0.702    0.483
## BrandAX          -9.43580   14.86814  -0.635    0.526
## BrandBB           3.26352   20.54206   0.159    0.874
## BrandBE          -4.70538   14.31167  -0.329    0.743
## BrandBV         -24.68019   19.71887  -1.252    0.212
## BrandCH         -13.64470   16.89896  -0.807    0.420
## BrandDG         -11.70667   14.43260  -0.811    0.418
## BrandDY          -2.10357   21.19808  -0.099    0.921
## BrandEA           3.85329   16.09139   0.239    0.811
## BrandHC          -3.04371   13.57381  -0.224    0.823
## BrandMK          -3.89967   13.81190  -0.282    0.778
## BrandMU         -13.94565   16.40345  -0.850    0.396
## BrandOJ         -13.25598   21.25816  -0.624    0.533
## BrandOO           2.54761   13.50548   0.189    0.850
## BrandOX           2.11429   14.18728   0.149    0.882
## BrandOY          -8.54102   14.02066  -0.609    0.543
## BrandPH         -13.08716   13.90990  -0.941    0.347
## BrandPO          -8.05111   19.03369  -0.423    0.673
## BrandPP         -11.38207   17.11624  -0.665    0.506
## BrandPR          -9.58384   13.47975  -0.711    0.478
## BrandPS         -19.73789   14.90218  -1.324    0.186
## BrandRA         -11.81135   20.90181  -0.565    0.572
## BrandRB           0.15690   13.14801   0.012    0.990
## BrandRJ         -16.69610   15.54028  -1.074    0.283
## BrandRL         -14.13335   15.54060  -0.909    0.364
## BrandRX          -4.14277   13.08811  -0.317    0.752
## BrandRY         -15.86872   13.22231  -1.200    0.231
## BrandSF         -12.07275   20.51086  -0.589    0.556
## BrandTF          -9.60295   14.21696  -0.675    0.500
## BrandTY         -17.47865   14.31132  -1.221    0.223
## BrandVA           2.48457   21.01856   0.118    0.906
## BrandVE          -6.00615   13.88764  -0.432    0.666
## BrandVO          -7.84678   14.36152  -0.546    0.585
## promoCODE F     -18.94262   26.34560  -0.719    0.473
## promoH15        -10.24686   24.67117  -0.415    0.678
## promoHC18       -30.08249   36.89893  -0.815    0.415
## promoLUX40       -2.95482   24.43458  -0.121    0.904
## promoNASC150     -6.15996   29.06656  -0.212    0.832
## promoNASC75     -20.32947   33.47197  -0.607    0.544
## promoNB         -14.42047   32.20278  -0.448    0.655
## promoNB40         8.05547   32.45870   0.248    0.804
## promoOO15        -9.87877   33.43834  -0.295    0.768
## promoOOX40        9.07036   29.26914   0.310    0.757
## promoOther       -4.59889   24.10023  -0.191    0.849
## promoOY12        -1.68345   33.55792  -0.050    0.960
## promoPB3         -5.89979   35.89489  -0.164    0.870
## promoPRE-SELL T   1.58530   32.90659   0.048    0.962
## promoPRE-SELL V   2.69695   42.56437   0.063    0.950
## promoPRE SELL T  -8.48946   33.32005  -0.255    0.799
## promoRB15         5.83293   28.61984   0.204    0.839
## promoRSD         12.36384   32.60438   0.379    0.705
## promoSUN1        31.21447   32.51273   0.960    0.338
## promoSY1         -3.24743   24.63739  -0.132    0.895
## promoSY100       -4.19219   24.48373  -0.171    0.864
## promoSY1000      -9.02390   27.02229  -0.334    0.739
## promoSY2         -7.78216   26.15571  -0.298    0.766
## promoSY200       -0.60026   25.81089  -0.023    0.981
## promoSY250        5.50742   24.76272   0.222    0.824
## promoSY5          1.01699   26.29332   0.039    0.969
## promoSYNERGY54  -12.69778   25.03677  -0.507    0.612
## promoSYVE         1.55493   25.47837   0.061    0.951
## promoUP1         -8.43329   24.65504  -0.342    0.733
## promoUP3        -16.34819   25.15020  -0.650    0.516
## promoVIP         11.54068   25.98017   0.444    0.657
## promoVP1200     -24.93114   33.35503  -0.747    0.455
## promoVPFP200      6.11276   25.25616   0.242    0.809
## promoWC1         16.71279   25.51141   0.655    0.513
## promoWild Card   -9.00834   27.75119  -0.325    0.746
## month2           -7.77109    5.25957  -1.478    0.140
## month3           -1.81593    5.45449  -0.333    0.739
## month4            3.52338    5.60733   0.628    0.530
## month5            2.47287    5.66723   0.436    0.663
## month6           -4.91644    5.22653  -0.941    0.347
## month7           -5.71545    6.65115  -0.859    0.391
## month8           -4.15867    5.32694  -0.781    0.435
## month9           -1.78900    5.43214  -0.329    0.742
## month10          -4.84808    5.70788  -0.849    0.396
## month11           2.82944    5.72757   0.494    0.622
## month12          -4.47122    5.85865  -0.763    0.446
## stateAL          -6.44711   25.79800  -0.250    0.803
## stateAR           4.55791   26.88410   0.170    0.865
## stateAZ           4.27815   22.42990   0.191    0.849
## stateCA           8.71411   21.16914   0.412    0.681
## stateCO          -2.18563   21.89649  -0.100    0.921
## stateCT          -0.98745   22.12531  -0.045    0.964
## stateFL           7.44931   21.29390   0.350    0.727
## stateGA           5.07439   21.68191   0.234    0.815
## stateGU          47.27253   31.17686   1.516    0.130
## stateHI          -6.74003   24.61812  -0.274    0.784
## stateIA           8.16987   24.47813   0.334    0.739
## stateID           3.05964   30.14644   0.101    0.919
## stateIL          -0.01358   21.59389  -0.001    0.999
## stateIN          -3.30616   22.87731  -0.145    0.885
## stateKS          -2.55266   22.50744  -0.113    0.910
## stateKY           4.00471   22.19660   0.180    0.857
## stateLA           6.71099   25.29071   0.265    0.791
## stateMA          -3.78333   22.73121  -0.166    0.868
## stateMD           5.02998   23.46099   0.214    0.830
## stateME          -4.42156   24.23415  -0.182    0.855
## stateMI          -5.03300   22.02199  -0.229    0.819
## stateMN          -5.31793   23.62548  -0.225    0.822
## stateMO          10.49268   22.95868   0.457    0.648
## stateMS          -2.06425   22.64035  -0.091    0.927
## stateMT           2.76483   25.87290   0.107    0.915
## stateNC          -0.08450   21.87626  -0.004    0.997
## stateND          -0.97132   30.59464  -0.032    0.975
## stateNE         -11.89414   23.49896  -0.506    0.613
## stateNH           1.09062   24.90381   0.044    0.965
## stateNJ           6.25181   21.68265   0.288    0.773
## stateNM          -1.33418   30.54518  -0.044    0.965
## stateNV           6.17007   22.59854   0.273    0.785
## stateNY           3.86561   21.33141   0.181    0.856
## stateOH          -2.11693   22.72454  -0.093    0.926
## stateOK           6.40163   22.49315   0.285    0.776
## stateOR           1.12752   22.83891   0.049    0.961
## statePA          -5.45929   21.71992  -0.251    0.802
## statePR          13.63346   22.64758   0.602    0.548
## stateRI          -1.12313   29.85211  -0.038    0.970
## stateSC          -5.70310   24.05793  -0.237    0.813
## stateTN           4.39440   22.94158   0.192    0.848
## stateTX           3.37447   21.21044   0.159    0.874
## stateUT          -9.07763   23.42049  -0.388    0.699
## stateVA          -4.93161   24.55915  -0.201    0.841
## stateVT          -1.69813   29.82681  -0.057    0.955
## stateWA          -6.56651   23.21941  -0.283    0.777
## stateWI          -8.05133   29.78809  -0.270    0.787
## stateWV          -1.75182   31.03483  -0.056    0.955
## stateWY          -9.00991   34.24992  -0.263    0.793
## 
## Residual standard error: 20.47 on 372 degrees of freedom
## Multiple R-squared:  0.2294, Adjusted R-squared:  -0.0337 
## F-statistic: 0.8719 on 127 and 372 DF,  p-value: 0.8179

# p-value: 0.08366 
lmdata<-na.omit(lm_cust_s2) 
lm_qbpms <-(lm(formula = Order_Qty ~  Qt + Brand + promo +  `Order Date`,   data = lm_cust_s2))
summary(lm_qbpms)

## 
## Call:
## lm(formula = Order_Qty ~ Qt + Brand + promo + `Order Date`, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.249  -8.121  -1.825   3.312 274.521 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)
## (Intercept)      9.367e+02  6.961e+02   1.346    0.179
## QtQ1_18          1.764e+01  1.845e+01   0.956    0.340
## QtQ2_17          2.488e+00  5.876e+00   0.423    0.672
## QtQ2_18          2.783e+01  2.126e+01   1.309    0.191
## QtQ3_17          1.228e+01  1.384e+01   0.887    0.375
## QtQ3_18          2.679e+01  2.462e+01   1.088    0.277
## QtQ4_17          1.311e+01  1.537e+01   0.853    0.394
## QtQ4_18          3.726e+01  2.765e+01   1.348    0.178
## BrandAX         -8.963e+00  1.418e+01  -0.632    0.528
## BrandBB         -7.788e+00  1.917e+01  -0.406    0.685
## BrandBE         -5.683e+00  1.346e+01  -0.422    0.673
## BrandBV         -1.389e+01  1.877e+01  -0.740    0.460
## BrandCH         -7.168e+00  1.606e+01  -0.446    0.656
## BrandDG         -1.157e+01  1.360e+01  -0.850    0.396
## BrandDY         -7.025e+00  1.897e+01  -0.370    0.711
## BrandEA          5.246e+00  1.526e+01   0.344    0.731
## BrandHC         -1.138e+00  1.274e+01  -0.089    0.929
## BrandMK         -4.354e+00  1.310e+01  -0.332    0.740
## BrandMU         -1.043e+01  1.580e+01  -0.660    0.509
## BrandOJ         -1.804e+01  1.694e+01  -1.065    0.288
## BrandOO          4.466e+00  1.272e+01   0.351    0.726
## BrandOX          2.964e+00  1.313e+01   0.226    0.821
## BrandOY         -5.354e+00  1.311e+01  -0.408    0.683
## BrandPH         -1.153e+01  1.295e+01  -0.891    0.374
## BrandPO         -1.582e+00  1.722e+01  -0.092    0.927
## BrandPP         -1.017e+01  1.593e+01  -0.639    0.523
## BrandPR         -5.565e+00  1.261e+01  -0.441    0.659
## BrandPS         -1.667e+01  1.419e+01  -1.174    0.241
## BrandRA         -1.371e+01  1.989e+01  -0.689    0.491
## BrandRB          9.941e-01  1.238e+01   0.080    0.936
## BrandRJ         -1.359e+01  1.479e+01  -0.918    0.359
## BrandRL         -1.493e+01  1.469e+01  -1.016    0.310
## BrandRX         -3.321e+00  1.237e+01  -0.268    0.789
## BrandRY         -1.330e+01  1.247e+01  -1.066    0.287
## BrandSF         -1.496e+01  1.875e+01  -0.798    0.425
## BrandTF         -6.670e+00  1.336e+01  -0.499    0.618
## BrandTY         -1.323e+01  1.376e+01  -0.962    0.337
## BrandVA         -7.796e+00  1.910e+01  -0.408    0.683
## BrandVE         -7.050e+00  1.310e+01  -0.538    0.591
## BrandVO         -7.115e+00  1.348e+01  -0.528    0.598
## promoCODE F     -5.408e+00  2.519e+01  -0.215    0.830
## promoH15        -4.563e-01  2.333e+01  -0.020    0.984
## promoHC18       -5.674e-01  3.413e+01  -0.017    0.987
## promoLUX40       8.297e+00  2.307e+01   0.360    0.719
## promoNASC150     1.146e+01  2.769e+01   0.414    0.679
## promoNASC75      7.210e-01  3.120e+01   0.023    0.982
## promoNB          6.543e+00  3.064e+01   0.214    0.831
## promoNB40        2.758e+01  3.079e+01   0.896    0.371
## promoOO15       -7.957e+00  3.067e+01  -0.259    0.795
## promoOOX40       1.546e+01  2.726e+01   0.567    0.571
## promoOther       2.207e+00  2.557e+01   0.086    0.931
## promoOY12        2.584e-01  3.064e+01   0.008    0.993
## promoPB3         4.475e+00  3.241e+01   0.138    0.890
## promoPRE-SELL T -3.141e+00  3.080e+01  -0.102    0.919
## promoPRE-SELL V  1.236e+01  3.338e+01   0.370    0.711
## promoPRE SELL T  6.725e+00  3.116e+01   0.216    0.829
## promoRB15        1.811e+01  2.718e+01   0.666    0.506
## promoRSD         2.192e+01  3.274e+01   0.669    0.504
## promoSUN1        4.260e+01  3.064e+01   1.390    0.165
## promoSY1         5.383e+00  2.604e+01   0.207    0.836
## promoSY100       5.135e+00  2.572e+01   0.200    0.842
## promoSY1000      4.657e+00  2.842e+01   0.164    0.870
## promoSY2         7.855e-01  2.733e+01   0.029    0.977
## promoSY200       1.929e+01  2.483e+01   0.777    0.438
## promoSY250       1.631e+01  2.624e+01   0.622    0.535
## promoSY5         8.146e+00  2.736e+01   0.298    0.766
## promoSYNERGY54  -6.864e+00  2.623e+01  -0.262    0.794
## promoSYVE        1.447e+01  2.697e+01   0.537    0.592
## promoUP1         3.317e+00  2.318e+01   0.143    0.886
## promoUP3        -3.213e+00  2.376e+01  -0.135    0.892
## promoVIP         1.868e+01  2.751e+01   0.679    0.498
## promoVP1200     -5.154e+00  3.045e+01  -0.169    0.866
## promoVPFP200     1.819e+01  2.353e+01   0.773    0.440
## promoWC1         2.403e+01  2.495e+01   0.963    0.336
## promoWild Card   4.344e+00  2.898e+01   0.150    0.881
## `Order Date`    -6.197e-07  4.681e-07  -1.324    0.186
## 
## Residual standard error: 20.02 on 424 degrees of freedom
## Multiple R-squared:  0.1595, Adjusted R-squared:  0.01078 
## F-statistic: 1.072 on 75 and 424 DF,  p-value: 0.3303

Assess the linear model

From above analyis I would use differnt model to valdiate the result. Lets take model lm_pbm which is model for promotion + brand + month would predict order Quanity.

To assess whether the linear model is reliable, we need to check for (1) linearity, (2) nearly normal residuals, and (3) constant variability. (4) Residuals are independent Residual = Observed value - Predicted value

# From above analyis I would use differnt model to valdiate the result. Lets take model lm_pbm which is model for promotion + brand + month would predict order Quanity .

# To assess whether the linear model is reliable, we need to check for 
#(1) linearity, 
#(2) nearly normal residuals, and 
#(3) constant variability. 
#(4) Residuals are independent
# Residual = Observed value - Predicted value 

library(DATA606)
plot_ss(x = lm_cust_s2$Order_Qty, y = lm_pbm$residuals,showSquares = TRUE)

## Click two points to make a line.
                                
## Call:
## lm(formula = y ~ x, data = pts)
## 
## Coefficients:
## (Intercept)            x  
##    -12.2794       0.8328  
## 
## Sum of Squares:  28156.54

# # (1) Linear association: The residuals plot shows a random scatter.
#Based on the plot we can clearly say that there is apparent pattern in the distribution as the numbers appear to be group and outlier are close to the regression line, so it can be treated as strong corelation and can be considered as a linear relationship.

# # (2) Nearly normal residuals: To check this condition, we can look at a histogram
hist(lm_pbm$residuals)

# or a normal probability plot of the residuals.
#It seems the plot is slightly skewed left, 
qqnorm(lm_pbm$residuals)
qqline(lm_pbm$residuals)  # adds diagonal line to the normal prob plot

# (3) we can say that its also  Nearly normal residuals even though its right skewed with few outliers . 
# (4)Residuals can be treated as independent as sample is drawn from independent .


# plot on sample
ggplot(data = lm_cust_s2,mapping = aes(y=lm_cust_s2$Order_Qty ,x= lm_cust_s2$promo))+ geom_point() + geom_smooth(method = "lm",se=FALSE) + geom_abline(slope = lm_pbm$coefficients[8], intercept = lm_pbm$coefficients[1], color="red")

# regression Line population data of 2 year.
(ggplot(data = mkt_Data,mapping = aes(y=mkt_Data$`Order Quantity` ,x= mkt_Data$`External Description`))+ geom_point() + geom_smooth(method = "lm",se=FALSE) + geom_abline(slope = lm_pbm$coefficients[8], intercept = lm_pbm$coefficients[1], color="red") )

# Lets plot on by Order Date 
# To assess whether the linear model is reliable, we need to check for 
#(1) linearity, 
#(2) nearly normal residuals, and 
#(3) constant variability. 
#(4) Residuals are independent
# 
plot_ss(x = lm_cust_s2$Order_Qty, y = lm_pd$residuals,showSquares = TRUE) #  Linear association

## Click two points to make a line.
                                
## Call:
## lm(formula = y ~ x, data = pts)
## 
## Coefficients:
## (Intercept)            x  
##    -13.7242       0.9308  
## 
## Sum of Squares:  13021.47

hist(lm_pd$residuals) # Right skewed 

qqnorm(lm_pd$residuals)
qqline(lm_pd$residuals) # very much on the regression line, Nearly normal residuals even though its right skewed

# On Sample

ggplot(data = lm_cust_s2,mapping = aes(y=lm_cust_s2$Order_Qty ,x= lm_cust_s2$`Order Date`))+ geom_point() + geom_smooth(method = "lm",se=FALSE) +
 geom_abline(slope = lm_pd$coefficients[8], intercept = lm_pd$coefficients[1], color="green")+
  geom_abline(slope = lm_pbm$coefficients[8], intercept = lm_pbm$coefficients[1], color="red")

# On Population 
ggplot(data = mkt_Data,mapping = aes(y = mkt_Data$`Order Quantity`,x= mkt_Data$Brand))+ geom_point() + geom_smooth(method = "lm",se=FALSE) +  geom_abline(slope = lm_pd$coefficients[8], intercept = lm_pd$coefficients[1], color="red") +
  geom_abline(slope = lm_pbm$coefficients[8], intercept = lm_pbm$coefficients[1], color="green")

plot(lm_pbm)

## Warning: not plotting observations with leverage one:
##   72, 100, 139, 196, 213, 217, 219, 414, 465, 470, 482

## Warning: not plotting observations with leverage one:
##   72, 100, 139, 196, 213, 217, 219, 414, 465, 470, 482

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

plot(lm_pd)

## Warning: not plotting observations with leverage one:
##   72, 100, 139, 196, 213, 217, 219, 414, 465, 470, 482

## Warning: not plotting observations with leverage one:
##   72, 100, 139, 196, 213, 217, 219, 414, 465, 470, 482

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## 
## Call:
## lm(formula = Order_Qty ~ promo + Brand + month, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.914  -8.133  -1.654   3.478 272.944 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)
## (Intercept)      26.13481   26.10286   1.001    0.317
## promoCODE F     -15.96890   25.23730  -0.633    0.527
## promoH15         -8.72719   23.45000  -0.372    0.710
## promoHC18       -19.24662   34.26227  -0.562    0.575
## promoLUX40        0.65737   23.17376   0.028    0.977
## promoNASC150     -1.28252   27.65930  -0.046    0.963
## promoNASC75     -14.85914   31.18716  -0.476    0.634
## promoNB          -6.14625   30.76470  -0.200    0.842
## promoNB40        15.07273   30.93316   0.487    0.626
## promoOO15       -16.15442   30.59427  -0.528    0.598
## promoOOX40        6.81802   27.41124   0.249    0.804
## promoOther       -3.73615   22.87707  -0.163    0.870
## promoOY12        -7.04911   31.00791  -0.227    0.820
## promoPB3         -6.01193   32.81257  -0.183    0.855
## promoPRE-SELL T  -4.13293   30.79075  -0.134    0.893
## promoPRE-SELL V   7.67132   33.41142   0.230    0.819
## promoPRE SELL T  -5.42158   31.26403  -0.173    0.862
## promoRB15         7.84967   27.13088   0.289    0.772
## promoRSD         16.07839   30.92792   0.520    0.603
## promoSUN1        29.85375   30.76470   0.970    0.332
## promoSY1          0.03163   23.35211   0.001    0.999
## promoSY100       -0.56330   23.22642  -0.024    0.981
## promoSY1000      -3.43163   25.67911  -0.134    0.894
## promoSY2         -4.81010   24.79152  -0.194    0.846
## promoSY200        8.62250   24.36471   0.354    0.724
## promoSY250        8.06814   23.49242   0.343    0.731
## promoSY5          3.93312   24.81882   0.158    0.874
## promoSYNERGY54   -9.85176   23.61471  -0.417    0.677
## promoSYVE         3.35126   24.29424   0.138    0.890
## promoUP1         -5.59888   23.29931  -0.240    0.810
## promoUP3        -13.01644   23.86255  -0.545    0.586
## promoVIP         14.93715   24.92897   0.599    0.549
## promoVP1200     -13.31577   30.77976  -0.433    0.666
## promoVPFP200     10.07814   23.99677   0.420    0.675
## promoWC1         17.74550   24.22135   0.733    0.464
## promoWild Card   -4.61956   26.46511  -0.175    0.862
## BrandAX         -10.95095   13.99807  -0.782    0.434
## BrandBB          -3.49403   19.13093  -0.183    0.855
## BrandBE          -4.82203   13.43485  -0.359    0.720
## BrandBV         -19.33190   18.85157  -1.025    0.306
## BrandCH         -10.45199   16.05497  -0.651    0.515
## BrandDG         -13.11649   13.48968  -0.972    0.331
## BrandDY          -6.86874   18.90344  -0.363    0.717
## BrandEA           4.50472   15.22928   0.296    0.768
## BrandHC          -2.81904   12.67625  -0.222    0.824
## BrandMK          -5.46062   13.01448  -0.420    0.675
## BrandMU         -12.97826   15.65353  -0.829    0.408
## BrandOJ         -17.12288   16.84112  -1.017    0.310
## BrandOO           2.50665   12.69621   0.197    0.844
## BrandOX           1.61952   13.06314   0.124    0.901
## BrandOY          -7.08570   12.97111  -0.546    0.585
## BrandPH         -11.87732   12.88164  -0.922    0.357
## BrandPO          -3.96044   17.19708  -0.230    0.818
## BrandPP         -13.70844   16.01366  -0.856    0.392
## BrandPR          -7.81338   12.60822  -0.620    0.536
## BrandPS         -17.09130   14.11834  -1.211    0.227
## BrandRA         -12.97364   19.96227  -0.650    0.516
## BrandRB          -0.59440   12.28941  -0.048    0.961
## BrandRJ         -15.00836   14.67000  -1.023    0.307
## BrandRL         -16.06863   14.66091  -1.096    0.274
## BrandRX          -4.88683   12.30268  -0.397    0.691
## BrandRY         -15.63530   12.40539  -1.260    0.208
## BrandSF         -17.20566   18.74432  -0.918    0.359
## BrandTF          -8.31906   13.32859  -0.624    0.533
## BrandTY         -14.79733   13.57891  -1.090    0.276
## BrandVA          -6.12332   19.06459  -0.321    0.748
## BrandVE          -8.31584   13.04585  -0.637    0.524
## BrandVO          -7.93330   13.45593  -0.590    0.556
## month2           -7.68282    4.89698  -1.569    0.117
## month3           -2.75872    5.08822  -0.542    0.588
## month4            2.54636    5.16142   0.493    0.622
## month5            0.60584    5.21460   0.116    0.908
## month6           -5.38599    4.82769  -1.116    0.265
## month7           -4.68335    6.21103  -0.754    0.451
## month8           -4.48277    4.89863  -0.915    0.361
## month9           -2.45666    5.05541  -0.486    0.627
## month10          -5.75226    5.33533  -1.078    0.282
## month11           2.15030    5.31743   0.404    0.686
## month12          -4.84616    5.42623  -0.893    0.372
## 
## Residual standard error: 20 on 421 degrees of freedom
## Multiple R-squared:  0.1672, Adjusted R-squared:  0.01286 
## F-statistic: 1.083 on 78 and 421 DF,  p-value: 0.3076

## $promo
##  [1] "CHANEL PRE" "CODE F"     "H15"        "HC18"       "LUX40"     
##  [6] "NASC150"    "NASC75"     "NB"         "NB40"       "OO15"      
## [11] "OOX40"      "Other"      "OY12"       "PB3"        "PRE-SELL T"
## [16] "PRE-SELL V" "PRE SELL T" "RB15"       "RSD"        "SUN1"      
## [21] "SY1"        "SY100"      "SY1000"     "SY2"        "SY200"     
## [26] "SY250"      "SY5"        "SYNERGY54"  "SYVE"       "UP1"       
## [31] "UP3"        "VIP"        "VP1200"     "VPFP200"    "WC1"       
## [36] "Wild Card" 
## 
## $Brand
##  [1] "AR" "AX" "BB" "BE" "BV" "CH" "DG" "DY" "EA" "HC" "MK" "MU" "OJ" "OO"
## [15] "OX" "OY" "PH" "PO" "PP" "PR" "PS" "RA" "RB" "RJ" "RL" "RX" "RY" "SF"
## [29] "TF" "TY" "VA" "VE" "VO"
## 
## $month
##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12"

## [1] "Regression Formula Y = 26.13 + -15.97 * promoCODE F + -8.73 * promoH15 + -19.25 * promoHC18 + 0.66 * promoLUX40 + -1.28 * promoNASC150 + -14.86 * promoNASC75 + -6.15 * promoNB + 15.07 * promoNB40 + -16.15 * promoOO15 + 6.82 * promoOOX40 + -3.74 * promoOther + -7.05 * promoOY12 + -6.01 * promoPB3 + -4.13 * promoPRE-SELL T + 7.67 * promoPRE-SELL V + -5.42 * promoPRE SELL T + 7.85 * promoRB15 + 16.08 * promoRSD + 29.85 * promoSUN1 + 0.03 * promoSY1 + -0.56 * promoSY100 + -3.43 * promoSY1000 + -4.81 * promoSY2 + 8.62 * promoSY200 + 8.07 * promoSY250 + 3.93 * promoSY5 + -9.85 * promoSYNERGY54 + 3.35 * promoSYVE + -5.6 * promoUP1 + -13.02 * promoUP3 + 14.94 * promoVIP + -13.32 * promoVP1200 + 10.08 * promoVPFP200 + 17.75 * promoWC1 + -4.62 * promoWild Card + -10.95 * BrandAX + -3.49 * BrandBB + -4.82 * BrandBE + -19.33 * BrandBV + -10.45 * BrandCH + -13.12 * BrandDG + -6.87 * BrandDY + 4.5 * BrandEA + -2.82 * BrandHC + -5.46 * BrandMK + -12.98 * BrandMU + -17.12 * BrandOJ + 2.51 * BrandOO + 1.62 * BrandOX + -7.09 * BrandOY + -11.88 * BrandPH + -3.96 * BrandPO + -13.71 * BrandPP + -7.81 * BrandPR + -17.09 * BrandPS + -12.97 * BrandRA + -0.59 * BrandRB + -15.01 * BrandRJ + -16.07 * BrandRL + -4.89 * BrandRX + -15.64 * BrandRY + -17.21 * BrandSF + -8.32 * BrandTF + -14.8 * BrandTY + -6.12 * BrandVA + -8.32 * BrandVE + -7.93 * BrandVO + -7.68 * month2 + -2.76 * month3 + 2.55 * month4 + 0.61 * month5 + -5.39 * month6 + -4.68 * month7 + -4.48 * month8 + -2.46 * month9 + -5.75 * month10 + 2.15 * month11 + -4.85 * month12 + e"

## 
## Call:
## lm(formula = Order_Qty ~ promo + `Order Date`, data = lm_cust_s2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.953  -8.500  -3.518   2.919 287.524 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      7.481e+01  1.359e+02   0.551   0.5822  
## promoCODE F     -1.667e+00  2.255e+01  -0.074   0.9411  
## promoH15         2.146e+00  2.083e+01   0.103   0.9180  
## promoHC18       -3.616e+00  2.853e+01  -0.127   0.8992  
## promoLUX40       9.065e+00  2.057e+01   0.441   0.6596  
## promoNASC150     1.178e+01  2.470e+01   0.477   0.6338  
## promoNASC75      1.268e+00  2.852e+01   0.044   0.9646  
## promoNB          1.238e+01  2.853e+01   0.434   0.6646  
## promoNB40        2.641e+01  2.853e+01   0.926   0.3550  
## promoOO15       -3.515e+00  2.853e+01  -0.123   0.9020  
## promoOOX40       2.281e+01  2.470e+01   0.923   0.3562  
## promoOther       6.914e+00  2.047e+01   0.338   0.7357  
## promoOY12        3.860e+00  2.852e+01   0.135   0.8924  
## promoPB3        -5.101e+00  2.852e+01  -0.179   0.8581  
## promoPRE-SELL T -2.047e+00  2.852e+01  -0.072   0.9428  
## promoPRE-SELL V  1.198e+01  2.852e+01   0.420   0.6746  
## promoPRE SELL T  5.342e+00  2.853e+01   0.187   0.8515  
## promoRB15        2.342e+01  2.471e+01   0.948   0.3438  
## promoRSD         3.372e+01  2.873e+01   1.174   0.2410  
## promoSUN1        4.838e+01  2.853e+01   1.696   0.0906 .
## promoSY1         1.127e+01  2.101e+01   0.536   0.5921  
## promoSY100       6.722e+00  2.049e+01   0.328   0.7430  
## promoSY1000      2.193e+00  2.349e+01   0.093   0.9256  
## promoSY2         8.096e+00  2.265e+01   0.357   0.7210  
## promoSY200       1.927e+01  2.160e+01   0.892   0.3728  
## promoSY250       1.669e+01  2.106e+01   0.792   0.4286  
## promoSY5         1.317e+01  2.269e+01   0.581   0.5618  
## promoSYNERGY54   3.545e+00  2.193e+01   0.162   0.8717  
## promoSYVE        1.438e+01  2.202e+01   0.653   0.5140  
## promoUP1         4.190e+00  2.064e+01   0.203   0.8392  
## promoUP3        -1.562e-01  2.115e+01  -0.007   0.9941  
## promoVIP         2.588e+01  2.241e+01   1.155   0.2488  
## promoVP1200      1.918e+00  2.852e+01   0.067   0.9464  
## promoVPFP200     1.891e+01  2.209e+01   0.856   0.3925  
## promoWC1         2.599e+01  2.162e+01   1.202   0.2300  
## promoWild Card   3.443e+00  2.346e+01   0.147   0.8834  
## `Order Date`    -4.493e-08  9.036e-08  -0.497   0.6193  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.16 on 463 degrees of freedom
## Multiple R-squared:  0.06917,    Adjusted R-squared:  -0.003208 
## F-statistic: 0.9557 on 36 and 463 DF,  p-value: 0.5453

## $promo
##  [1] "CHANEL PRE" "CODE F"     "H15"        "HC18"       "LUX40"     
##  [6] "NASC150"    "NASC75"     "NB"         "NB40"       "OO15"      
## [11] "OOX40"      "Other"      "OY12"       "PB3"        "PRE-SELL T"
## [16] "PRE-SELL V" "PRE SELL T" "RB15"       "RSD"        "SUN1"      
## [21] "SY1"        "SY100"      "SY1000"     "SY2"        "SY200"     
## [26] "SY250"      "SY5"        "SYNERGY54"  "SYVE"       "UP1"       
## [31] "UP3"        "VIP"        "VP1200"     "VPFP200"    "WC1"       
## [36] "Wild Card"

anova(lm_pbm,lm_pd)

Evaluation of the Model

Using test and sample data we will see how good our Model is. We wil luse Absolute Mean error of the model and decide which regression models works well for the sample.

# lm_cust_s2 
# lm_cust_s2 <- lm_cust[sample(nrow(lm_cust),500),]
#  lm_cust_s2$month <- month(lm_cust_s2$`Order Date`)
#  lm_cust_s2$month <- as.factor(lm_cust_s2$month )
#  names(lm_cust_s2)
#  

# Uisng same sample to test lm_cust_s2 , creating sample of 500 more to test.

lm_cust_t1  <- lm_cust_s2
lm_cust_t2 <- lm_cust[sample(nrow(lm_cust),500),]
 lm_cust_t2$month <- month(lm_cust_t2$`Order Date`)
 lm_cust_t2$month <- as.factor(lm_cust_t2$month )
 names(lm_cust_t2)

##  [1] "KUNNR_NEW"  "Qt"         "Brand"      "Order Date" "promo"     
##  [6] "city"       "state"      "Order_Qty"  "Doll_Val"   "month"

 lm_pbm1 <-  update(lm_pbm,lm_cust_s2)
 
 
 # Predict main train data
lm_pred_pbm <- predict(lm_pbm,lm_cust_t1)
lm_pred_pd <- predict(lm_pd,lm_cust_t1)
lm_pred_qbpms <- predict(lm_qbpms,lm_cust_t1)


mean(abs(lm_cust_t1$Order_Qty- lm_cust_t1$Order_Qty))

## [1] 0

mean(abs(lm_pred_pbm - lm_cust_t1$Order_Qty))

## [1] 9.284085

mean(abs(lm_pred_pd - lm_cust_t1$Order_Qty))

## [1] 9.7031

mean(abs(lm_pred_qbpms - lm_cust_t1$Order_Qty))

## [1] 9.31299

# Using test data of new set
# lm_pbm <- lm(formula = Order_Qty ~ promo + Brand + month, data = lm_cust_t2)

update

## standardGeneric for "update" defined from package "stats"
## 
## function (object, ...) 
## standardGeneric("update")
## <environment: 0x000000001075c9b8>
## Methods may be defined for arguments: object
## Use  showMethods("update")  for currently available ones.

lm_pred_pbm <- predict(lm(formula = Order_Qty ~ promo + Brand + month, data = lm_cust_t2),lm_cust_t2)
lm_pred_pd <- predict(lm(formula = Order_Qty ~ promo + `Order Date` , data = lm_cust_t2),lm_cust_t2)
lm_pred_qbpms <- predict(lm(formula = Order_Qty ~ Qt + Brand+promo +month+ state , data = lm_cust_t2),lm_cust_t2)

## Warning in predict.lm(lm(formula = Order_Qty ~ Qt + Brand + promo + month
## + : prediction from a rank-deficient fit may be misleading

mean(abs(lm_cust_t2$Order_Qty- lm_cust_t2$Order_Qty))

## [1] 0

mean(abs(lm_pred_pbm - lm_cust_t2$Order_Qty))

## [1] 7.633058

mean(abs(lm_pred_pd - lm_cust_t2$Order_Qty))

## [1] 8.786852

mean(abs(lm_pred_qbpms - lm_cust_t2$Order_Qty))

## [1] 7.365802

From above mean errors we can see that model 1 with regession model with formula lm(formula = Order_Qty ~ promo + Brand + month, data = lm_cust_t2) is well close to zero in terms of mean absulate error.